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TRANSCRIPT
I. II. III. IV. V. VI. VII. VIII. IX.
“Education is not the learning of many facts but the training of the mind to think.” – Albert Einstein
To all Acadecers, Decathletes, and lovers of learning: I welcome you to the wonderful world of energy
science that awaits you within the pages of this year’s Science Power Guide. Covering topics as diverse
as quantum physics, radiation physics, and nuclear physics, this year’s Science Guide will teach you
about how mankind unlocked the power of the atom.
I, Jerry Zhao, former Decathlete of North Penn High School, will be your guide through this broad and
diverse field. I have always been fascinated by the physical sciences, humanity’s continual attempt to
explain the unexplainable and to understand the world around us. I hope that reading this guide will
inspire you to further your studies in the applied sciences.
This Power Guide will go above and beyond USAD in presenting information in a cleanly organized,
comprehensive, and easily searchable format. Since many concepts in this packet pertain to multiple
branches of science, I have done my best to present the big picture while remaining faithful to the
all-important details.
I have bolded key concepts, numbers, laws, names, dates, as well as any term bolded in the official
USAD Resource Guide. For your convenience, all bolded terms have been carefully tabulated and
organized in the Power Lists at the back of this guide.
Since USAD cannot possibly cover all concepts important to the field of nuclear science in the
Resource Guide, I have made it a point to identify and correct any gaps in information through the
addition of footnotes. While these footnotes are not testable material, they will add helpful contextual
information that will give you a better grasp of the subject material. Any contextual information I
include in a footnote will start with “Enrichment Fact:”
To ease the tediousness of this Power Guide, I have included my humorous comments and wry
remarks on the subject material in the footnotes as well. While you may be entertained by my feeble
attempts at comedy, you may choose to save yourself the pain by skipping any footnote which I have
signed with my name. I promise I won’t be offended.
I hope this Power Guide serves you well in your exploitation of nuclear science. The topics presented
here will help you in competition and beyond.
Happy studying!
Jerry Zhao
This year’s Science Resource Guide covers the history of atomic theory, quantum theory,
radioactivity, nuclear fission and fusion, and the development of the atomic bomb.
Section I covers 35% of the curriculum and 30% of the test material. This section walks you
through the history of classical atomic theory and discusses the phenomena that form the
foundation of modern quantum theory.
Section II covers 24% of the curriculum and 30% of the test material. This section discusses
the structure of atoms and the causes and effects of radiation.
Section III covers 20% of the curriculum and 25% of the test material. This section discusses
the science and applications of nuclear fusion and fission.
Section IV covers 21% of the curriculum and 15% of the test material. This section focuses
primarily on the Manhattan project and the development of the atomic bombs.
Classical Atomic Theory Foundations of atomic theory
Atomic theory describes the atom, the universe’s basic building block
The first atomic models were rooted in classical1 physics
Today, quantum theory informs our current models
Natural philosophers developed atomic theory in the 5th century BCE
They believed matter to be composed of indivisible particles
The earliest references to atoms came from Democritus and Leucippus
Plato proposed four fundamental types of particles: fire, water, earth, and air2
He later added a fifth fundamental element, aether
Each particle had a unique shape that represented its properties
Water flowed easily
It hence formed an almost-spherical isocahedron
Earth formed a cube since it was packed and solid
The word “atom” comes from the Greek “atomos”, meaning “unable to be cut”
These philosophers could not test any of their theories
In the third century BCE, Aristotle proposed an opposing idea
He described the basic elements as infinitely divisible
Different ratios of the four elements resulted in different materials
Aristotle’s anti-atomist views lasted into the 17th century
In the 11th century, the study of atomism shifted from Europe to India
The Middle Ages in Europe saw a decline in scientific thinking
Islamic scholars combined Greek and Indian ideas in the Golden Age of Islam
Their ideas formed the Asharite3 school of theology
It returned to Europe in the Renaissance through Catholic priest Pierre Gassendi
Gassendi reconciled atomism with the Catholic church
He often discussed atomic theory with the philosopher Rene Descartes4
Galileo Galilei also supported atomist views
In the 17th century, Robert Boyle challenged atomic theory with corpuscular theory
1
2
3
4
Corpuscules5 are divisible particles which alter the properties of matter
Isaac Newton promoted corpuscular theory in his 1704 book Opticks
According to him, corpuscules made up all light
In the 18th century, scientists first uncovered the principles of chemical reactions
French chemist Antoine Lavoisier6 created the first list of elements
He identified and named hydrogen and oxygen
Lavoisier also discovered that mass is conserved in chemical reactions
𝑀𝑎𝑠𝑠 𝑜𝑓 𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 = 𝑀𝑎𝑠𝑠 𝑜𝑓 𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠
French chemist Joseph Proust discovered that elements combine in fixed ratios
In 1864, Dmitri Mendeleev created the periodic table of elements
He arranged 64 known elements by their atomic weights
Other atomic properties had not been discovered yet
The periodic table predicted the existence of still-to-be-discovered gallium
Modern theories of the atom
English chemist John Dalton penned the first principles of atomic theory
He borrowed ideas from Lavoisier and Proust
In 1808, he published his ideas in A New System of Chemical Philosophy
Dalton also tabulated atomic weights
Dalton’s Atomic Principles
• Elements are composed of atoms
• Atoms of the same element are completely identical
• Atoms cannot be created, destroyed, or divided
• Atoms react in simple ratios to form compounds
• Atoms recombine in chemical reactions
The development of the cathode ray tube allowed for many new observations
Michael Faraday observed that a voltage between a cathode and anode caused the
anode to glow
The anode holds a positive charge, while the cathode holds a negative
Negatively charged particles accelerate
between the cathode and anode
These particles form a cathode ray7
Televisions and computer monitors
display images using cathode rays8
In 1897, J.J. Thomson measured the mass
of a cathode ray particle
He found them to be 1800 times less
massive than hydrogen
These negatively charged particles
are now called electrons
Thomson also proposed that atoms
contained smaller particles like electrons in his plum pudding model
5
6
7
8
Electrons float around within the atom, like plums in plum pudding
Hans Geiger and Ernest Marsden were Ernest Rutherford’s research partners
In 1911, Geiger and Marsden conducted the gold foil experiment
They directed a beam of positive particles at a sheet of gold foil
They expected the beam to pass straight through because the electrons in the gold
foil would be very small
Instead, the gold foil deflected many of the particles in the ray at extreme angles
Rutherford described the result as if “a 15-inch shell at a piece of tissue paper and
it came back and hit you”
In response to this experiment, Rutherford designed a new model
He placed a dense nucleus at the atom’s core
Since the positively charged ray was sometimes
deflected backwards, the nucleus must be positively
charged
He described the atom as a planetary system, with
electrons orbiting the nucleus
Rutherford’s model had two inconsistencies
Thermally excited atoms do not emit radiation at every
frequency
According to classical physics, the electrons should
eventually fall into the nucleus
Early Quantum Theory Wave Theory of Light
Many scientists also argued over whether light is a particle
or a wave
Isaac Newton supported the corpuscular theory of light
In his 1704 book Opticks, he described light as small
particles
The corpuscular theory explained reflection, but not
refraction or diffraction
The Dutch physicist Christiaan Huygens believed that light contained waves
The wave theory explained how light diffracts around corners
Optical experiments confirmed light’s wave-like properties
In 1803, Thomas Young noted that two parallel slits cause alternating bands of light
and dark on a screen
He called this phenomenon double slit diffraction
It results from constructive and destructive interference from light waves
Sound waves produce a similar effect9
In the late nineteenth century, James Clerk Maxwell theorized electromagnetism
He described light as a wave of oscillating electric and magnetic fields
Modern scientists now understand that visible light forms only a small portion of the
electromagnetic spectrum
All electromagnetic waves travel at the speed of light
9
Different types of waves differ in their frequencies and wavelengths
Frequency measures oscillations per second in Hertz (Hz)
Wavelength measures the distance between oscillations
High frequency waves have low wavelengths
Blackbody Radiation
All matter releases energy in the form of thermal radiation
The intensity of radiation is proportional to the temperature of the object
At room temperature, thermal radiation remains invisible in the infrared band
Around 1000 K, the thermal radiation
enters the visible band
For example, metals glow red-hot
According to the classical explanation,
oscillating atoms act as “antennas” which
project radiation
Blackbodies are theoretical objects which
absorb all incoming radiation
Blackbodies remain in equilibrium by
constantly emitting thermal radiation
The ultraviolet catastrophe refers to a gap
between classical expectations and
experimental observations10
According to classical theory, the intensity of
thermal radiation should reach infinity as
wavelength decreases
However, experimental results showed that
thermal radiation contains less wavelengths below ultraviolet than expected
Energy Quantization
Quantization refers to the discretization of possible energy levels
Instead of existing at a continuous range of possible energies, a particle could only
exist at certain specific energy levels
A quantum of energy describes the smallest energy level a particle could have
All other energy levels are multiples of this fundamental quantum
German scientist Max Planck first proposed energy quantization in 1900
Planck’s Formula
𝐸 = ℎ𝑓𝑛
𝐸 = Energy ℎ = 6.63 × 10−34 𝐽 ⋅ 𝑠 = Planck’s constant
𝑓 = Frequency of oscillation 𝑛 = 1, 2, 3 … = the quantum number
Since the quantum of energy is tiny, quantization is difficult to detect
The Photoelectric Effect
Heinrich Hertz discovered in 1887 that shining ultraviolet light on a metal will cause it to
emit electrons
This phenomenon is the photoelectric effect
J.J. Thomson identified the emitted particles as electrons
10
Using classical theory, they reasoned that ultraviolet waves “charged” the electrons of
the atom with energy
After enough energy transfer, the electrons would escape
In 1900, Philippe Lenard observed contradictions to the classical theory
Classical Expectation Experimental Observation
Time delay during which the electron gains
energy before it is ejected Electron ejection happens instantaneously
Any frequency of light should cause electron
emission if the light intensity is high enough
Only light above a certain frequency could
cause electron emission
Increasing light intensity increases the energy
of ejected electrons
Increasing light intensity had no effect on
electron energy
Light frequency has no effect on electron
energy
Increasing light frequency increased electron
energy
Albert Einstein proposed the quantization of light energy in 1905
The massless photon is the smallest quantum of light
Photons have energy on the order of 10−19 𝐽
Though massless, photons possess
momentum11
In the photoelectric effect, photons collide with
electrons, ejecting them from the metal
Einstein earned the 1921 Nobel Prize for this
insight
In 1923, American physicist Arthur Compton noticed
that X-rays scatter upon impact with an electron
This Compton scattering provided further proof
for light quantization
Atomic Spectra
Elements emit their own unique atomic spectra of light when excited
A spectrum describes a set of frequencies of light
Atomic spectra act as “fingerprints” that can be used to identify an element
In the 1800s, atomic spectroscopy was developed
The technique identifies a sample’s chemical composition
In 1868, scientists used atomic spectroscopy to identify helium in the sun
Helium was only discovered on Earth 30 years later
An emission spectrum describes the set of frequencies emitted by an excited atom
A spectroscope uses a prism to separate the emission into wavelengths
Passing white light through a set of atoms creates an absorption spectrum
Lines in the spectrum mark which frequencies were absorbed
Generally, the absorption spectrum marks the gaps in the emission spectrum
In 1885, Swiss physicist Johann Balmer found a relationship between the frequencies of
hydrogen’s emission spectrum
Johannes Rydberg used Balmer’s findings in formulating the Rydberg formula
11
𝟏
𝝀= 𝑹𝑯 (
𝟏
𝒎𝟐−
𝟏
𝒏𝟐)
𝝀 = wavelength of emitted
light
𝑹𝑯 = 𝟏. 𝟎𝟗𝟕 × 𝟏𝟎𝟕 𝒎−𝟏 = the
Rydberg constant 𝒎, 𝒏 = positive integers
The Bohr Model
In 1913, Danish physicist Neils Bohr created an atomic model that accounted for energy
quantization
He modified Rutherford’s solar system model
The electron’s angular momentum now had to be a multiple of ℎ
2𝜋
Bohr had no experimental justification for this change
Luckily, it worked anyway
Bohr’s model has the following properties:
Electrons move in circular orbits around the nucleus
Only certain orbits, or energy levels, are stable
Electrons do not radiate energy in their orbits
This assumption contradicted known physical laws of physics12
Electrons can move between energy levels
Absorbing radiation increases the energy level
Emitting radiation decreases the energy level
Electron Quantum Principles
Quantum
number, n
Electron’s potential energy levels
Ground state: n = 1, electron closest to nucleus
n > 1 → excited states
Ionization energy Energy needed to remove an electron
Hydrogen: 13.6 eV
Electron’s
distance from
nucleus at each
level
𝒓𝒏 = 𝒏𝟐𝒂𝟎
n = quantum number
𝑎0 = 0.0529 𝑛𝑚 = ground state electron radius
= the Bohr radius
Electron’s energy
at each energy
level
𝑬𝒏 =−(𝟏𝟑. 𝟔 𝒆𝑽)
𝒏𝟐
eV, or electron volt, = energy of one electron
accelerated through a 1V potential difference
1 𝑒𝑉 = 1.6 × 10−19 𝐽
The negative sign implies that attraction keeps
the electron around the nucleus
Bohr’s model explained why the Rydberg formula worked
𝑚 and 𝑛 correspond to the energy levels between which an electron transitions
Lines in the emission spectrum had corresponding quantum numbers
12
Series Balmer Lyman Paschen
Discovered 1906-14 1908
State transition 𝑛 > 2 → 𝑛 = 2 𝑛 > 1 → 𝑛 = 1 𝑛 > 3 → 𝑛 = 3
Bohr’s correspondence principle reconciled quantum and classical physics13
At high quantum numbers, quantum and classical predictions should match
In the Bohr model, emissions at high quantum numbers match the electron’s orbital
frequency
In 1914, James Franck and Gustav Hertz found evidence supporting the Bohr model
They fired electrons through mercury gas in a heated tube
The electrons lost energy in quantized amounts of factors of 4.9 eV
Franck and Hertz found that mercury emits ultraviolet radiation with similarly
quantized amounts
They won the 1925 Nobel Prize in Physics for this work
The Bohr model still had several faults
It could only describe the behavior of electrons in hydrogen
The model did not explain why some lines in hydrogen’s atomic spectrum are actually
two very closely spaced lines
It did not account for molecule formation
Particles as Waves The de Broglie Hypothesis
French physicist Louis de Broglie first proposed the wave behavior of matter in his 1924
Ph.D. dissertation
He compared the wave-particle behavior of light and the behavior of matter
de Broglie Hypothesis
𝜆 =ℎ
𝑝
𝒉 = Planck’s constant 𝑝 = particle momentum 𝜆 = de Broglie wavelength
It explained why electron angular momentum must be quantized
If the electrons are instead waves, their wavelengths must be factors of their orbital
circumference
In 1927, Bell Labs researchers confirmed the de Broglie hypothesis
Clinton Davisson and Lester Germer observed a diffraction pattern when firing
electrons at nickel
They wanted to quantify the roughness of the crystalline nickel
Since only waves can diffract, the electrons must have wavelike behavior
Many innovations rely on this finding
13
Transmission electron microscopes (TEMs) use the wave behavior of electrons to
achieve very high resolutions
Light microscopes cannot resolve objects less than 500 nm, the approximate
wavelength of visible light
A TEM accelerates electrons with a
wavelength of 0.0037 nm to 100 keV
We do not observe the wave behavior of matter
in everyday life
Planck’s constant is very small
An apple has a de Broglie wavelength a
trillion trillion times smaller than an atom
Wave-Particle Duality
Wave-particle duality refers to the wave-particle
behavior of both light and matter
Electrons, photons, and neutrons all create a
diffraction pattern in Young’s double slit
experiment
The experiment cannot detect the path of
any individual particle
In 1926, Albert Einstein14 wrote to Max Born about the strangeness of quantum
mechanics
He said that he could not believe God would play at dice
Modern Quantum Mechanics Quantum Mechanics
Quantum mechanics emerged in 1925 to unify quantum theory
Classical physics had a set of laws to describe wave and particle interactions
Newton’s laws described particle interactions
The differential wave equation described wave behavior
In 1925, Austrian physicist Ernst Schrödinger designed an equation that describes the
wave-like behavior of particles
The Schrödinger equation cannot be derived from existing theorems
It has received experimental verification
It’s solutions of wave functions are labeled by the Greek letter psi (𝜓 𝑜𝑟 Ψ)
In 1926, Max Born suggested that Ψ2 = the probability distribution of a particle
Two wave functions have particular importance
A wave “packet” describes a particle freely travelling through space
A “particle-in-a-box” describes a particle trapped in an infinite potential well
Its energy levels depend on the mass of the particle and the size of the box
The Schrödinger equation suggests particles can escape potential wells with quantum
tunneling
Classical physics thought that a particle cannot cross potential barriers if its energy is
too low
Particles actually have a non-zero probability of crossing potential barriers
14
The scanning tunneling microscope (STM) uses quantum tunneling
The STM forms a potential barrier between the microscope and the sample
It analyzes the current based on tunneling electrons with a resolution of 0.1 nm
Quantum Probability
In 1935, Schrödinger presented the Schrödinger’s cat scenario
It showed that a quantum system can exist in multiple states before being observed
A cat is placed inside a box with a container of poison
The poison has a 50% chance of being released
Until someone opens the box, the cat is said to be both dead and alive
Newtonian mechanics Quantum mechanics
The world is deterministic The world is probabilistic
Object positions are predictable and
determined
Repeated measurements of an object yield different
results
Works at larger scales Observed at the subatomic scale
At large scales, uncertainty in measurements comes from the measuring instrument
Quantum mechanics sets an upper limit on the precision of any measurement
Measuring an object alters the object
Ex: shooting a photon at a particle alters the particle’s position and velocity
German physicist Werner Heisenberg proposed the Heisenberg uncertainty principle
in 1927
It states the impossibility of knowing a particle’s exact position and momentum
Increasing the precision of one measurement decreases that of the other
Heisenberg uncertainty principle: 𝚫𝒙𝚫𝒑 ≥𝒉
𝟐𝝅
Δ𝑥 = uncertainty in position Δ𝑝 = uncertainty in
momentum ℎ = Planck’s constant
Because the value of Planck’s constant is so small, the uncertainty principle only affects
microscopic measurements
In 1940, George Gamow wrote the book Mr. Tompkins in Wonderland
It describes a world with a very large Planck’s constant
A bank teller explored a “quantum jungle”
Elephants have fuzzy skin from uncertainty in their position
A gazelle spread out into a herd as if diffracted through a bamboo forest
The Modern Quantum Model
The modern model of the atom is the Schrödinger model
Wave functions describe the electron’s waveform
The amplitude of the wave function at a position describes the probability of
finding an electron at that position
Electrons orbit the nucleus in a probability cloud
The probability could does not need to be spherical
Bohr radii represent their probable positions
Three quantum numbers describe the electron’s position
The principal quantum number, Bohr’s original number, is 𝑛
This number describes the energy of the electron
The orbital quantum number is ℓ where 0 ≤ ℓ ≤ 𝑛 − 1
Electrons with the same ℓ and 𝑛 occupy the same subshell
Orbital quantum number 0 1 2 3
Subshell s p d f
Subshells can be described using their principle quantum number and letter
Ex: Subshell 3d has electrons with 𝑛 = 3, ℓ = 2
Superscripts denote electron configurations
Sodium’s electron configuration is 1𝑠22𝑠22𝑝63𝑠2
The orbital magnetic quantum number is 𝑚ℓ, −ℓ ≤ 𝑚ℓ ≤ ℓ
The magnetic quantum number affects an atom’s behavior in a magnetic field
The Zeeman effect alters the energy of electrons with differing 𝑚ℓ values
Some spectral lines are actually two lines with slightly differing frequencies
The spin quantum number 𝑚𝑠 does not come from the Schrödinger equation
In 1925, scientists observed the yellow emission lines of sodium splitting
This effect was called fine structure splitting
In 1928, Paul Dirac derived a relativistic form of the Schrödinger equation
It derives the spin quantum number from the electron’s angular momentum
Electrons are a type of fermion, particles with half-integer spin
Electrons can have 𝑚𝑠 =1
2 or −
1
2
Usually, the spin is characterized as “spin up” or “spin down”
Note that the spin number does not refer to the actual spinning motion
The electron would have to spin faster than the speed of light if so
The spin direction describes the electron’s contribution to the magnetic field
The magnetic moment measures electrons’ tendency to align with the magnetic
field
Types of elements
Diamagnetic • Shells are filled with electrons; electron spins cancel to 0
• Element is repelled by a magnetic field
Paramagnetic
• Shells are partially filled; electron spins do not cancel out
• Atoms in the element align to a magnetic field
• Atoms de-align when removed from the field
Ferromagnetic
(iron, nickel)
• Shells are partially filled
• Atoms in the element align, even without a magnetic field
• Used in permanent magnets
• Above the Curie temperature, magnetic properties are lost
An electron’s state can be described by the four quantum numbers, 𝑛, ℓ, 𝑚ℓ, and 𝑚𝑠
Wolfgang Pauli proposed the Pauli exclusion principle
No two electrons in an atom have the same four quantum numbers
No two fermions can occupy the same quantum state
Hence, electrons added to the atom fall to the lowest energy quantum level
This property explains why noble gases like neon and helium do not react easily
They have filled electron shells15
Alkali metals such as lithium and sodium, however, are extremely reactive
They have unpaired electrons
The Pauli exclusion principle does not apply to bosons
Bosons are particles with integer spin, not half-integer spin
In 1924, Satyendra Bose and Albert Einstein suggested that cooling a gas of bosons
to 0 K would create a new state of matter
This temperature is also known as absolute zero
The “K” stands for “Kelvin”
In 1995, Carl Weiman and Eric Cornell produced this new state of matter with laser
cooling
They called it the Bose-Einstein condensate
Applications of Atomic Physics Lasers
Atoms emit energy when an electron falls from a higher to lower energy level
In spontaneous emission, the atom emits a photon in a random direction
The atom remains excited for a few nanoseconds
In stimulated emission, a passing photon can prompt a second photon release
The passing photon’s oscillating electric field must have the same frequency as the
transition frequency of the excited electron
The second emitted photon oscillates in synchrony with the first
Laser stands for Light Amplification by Stimulated Emission of Radiation
Lasers were first designed in 1960
A reflective cavity contains and amplifies emitted light of uniform wavelength
It creates a chain reaction of stimulated emissions
A laser’s power ranges from 0.001 watts to 10,000 watts
Lasers are widely used in medicine, industry, and research16
Qualities of Lasers Qualities of Ordinary Light and Radiation
Monochromatic: carry one light
frequency Carry many different frequencies
Directional: do not spread as they
travel Decrease in intensity with distance squared
Coherent: waves travel in the same
phase17, so they exhibit cleaner
interference effects
Do not travel in the same phase (ordinary
light)
Materials used in the laser must meet two requirements
The element’s excited state must be metastable
It has to remain excited state for some time before falling to the ground state
Simulated emission can then occur before spontaneous emission
Most of the atoms in the laser need to be in the excited state
15
16
17
A process called population inversion creates a sample that contains more atoms
in the excited state
A common design is the Helium-Neon (HeNe) laser
HeNe lasers produce bright red 632.8 nm light
HeNe lasers are used in physics18 demonstrations and barcode scanners
Helium atoms excited by an electric current collide with neon atoms
The neon atoms emit 632.8 nm radiation
Laser cooling uses lasers to slow down the movement of atoms
Room temperature gas particles move at 500 m/s
Quantum effects cannot be easily observed at these speeds
The scientific community awarded the 1997 Nobel Prize in Physics to the three
scientists who developed laser cooling
Laser cooling relies on two principles
(1) Conservation of momentum implies that each photon from the laser carries
some momentum to the gas particle it strikes
The laser exerts an overall pressure on the gas particle
(2) The Doppler effect describes how moving towards or away from a wave source
alters the apparent frequency and wavelength
A siren moving towards you sounds high pitched, while a siren moving away
from you is low pitched
The cooling laser has a frequency slightly below the transition’s
Only particles moving towards the laser will be excited and slowed
Systems involve six laser beams
Two beams point in opposite directions along the x, y, and z axes
In 2015, Stanford scientists cooled a sample of gas to 50 trillionths of a kelvin
A rubidium atom at this temperature moves at 70 thousandths mm/se
Atomic Clocks
Atomic clocks use the timings of atomic transitions to tell time
Unlike pendulum clocks, they do not respond to environmental changes
Atomic transition timings will be identical for all atoms of an element
In 1955, the first atomic clock was created using cesium
This clock had an error of 1 second per 300 years
Modern cesium clocks are accurate to 1 second per 300 million years19
The accuracy of frequency measurements and ability to remove measurement
noise have improved
In 1967, the second was redefined as the time that elapses during 9,192,631,770 hyperfine
transitions of cesium-137
Hyperfine energy level differences result from magnetic interactions between
electron spin and nuclear spin in the ground state
The second has become the most accurately defined SI unit of measurement
Elements used in atomic clocks include hydrogen, rubidium, mercury, strontium, and
aluminum
The National Institute of Standards and Technology uses cesium-13
18
19
Structure of the Nucleus Discovery of the Proton and Neutron
Ernest Rutherford performed the gold foil
experiment in 1911
He discovered the presence of a small, dense,
positively charged core at the center of the
atom
In 1917, Rutherford carried out particle scattering
with nitrogen gas
He was surprised to notice hydrogen nuclei
being produced from the collision
He decided that the hydrogen nucleus
must be a fundamental building block of
matter
Later scientists realized that the nucleus
contains just a single proton
Surprisingly, the nucleus did not have a charge proportional to its mass
He suggested that the nucleus contained neutral proton-electron pairs
However, electrons cannot exist inside the nucleus
According to the Heisenberg uncertainty principle, the electron has a minimum
energy in the nucleus
It exceeded experimentally observed electron energies
Experimental observations of nuclear spin also contradict this idea
In 1920, Rutherford that proton-electron pairs merge into neutrons
In 1930, scientists found the neutron when bombarding beryllium with alpha particles
The beryllium emitted neutral highly penetrating radiation
This radiation did not behave like photons
It had enough energy to eject photons from paraffin (wax)
English scientist James Chadwick confirmed this particle was the neutron in 1932
Nuclear Properties
Nuclear physics studies the structure and interactions of the atomic nucleus
Nuclei consist of protons and neutrons, known collectively as nucleons
Protons have a positive charge of +𝟏. 𝟔 ⋅ 𝟏𝟎−𝟏𝟗 Coulombs
Neutrons have a negative charge and a slightly higher mass than protons
Nuclei are notated by their numbers of neutrons and protons
Nuclear notation: 𝑿𝒁𝑨
X Chemical symbol
Z
Atomic number - number of protons
Unique to each element; can be omitted from notation e.g. uranium 238 = uranium with
atomic mass 238
N Number of neutrons
A Atomic mass number, Z + N – total number of neutrons and protons
Always an integer
The relative mass number describes the average atomic mass of an element
This number appears on periodic tables20
It refers to the average atomic mass of all isotopes of an element, weighted by the
abundance of each isotope
Atomic masses are measured in unified mass units, u
The 𝑀𝑒𝑉
𝑐2 unit of mass comes from Einstein’s relation 𝐸 = 𝑚𝑐2
𝟏 𝒖 =𝟏
𝟏𝟐 mass of 𝑪𝟏𝟐 = 𝟏. 𝟔𝟔 × 𝟏𝟎−𝟐𝟕 𝒌𝒈 = 𝟗𝟑𝟏. 𝟒𝟗
𝑴𝒆𝑽
𝒄𝟐
Weight in Kilograms Unified Mass Units (u) 𝑴𝒆𝑽
𝒄𝟐
Proton 1.672 × 10−27 1.007276 (~1 u) 938.28
Neutron 1.675 × 10−27 1.008665 (~1 u) 939.57
Electron 9.109 × 10−31 5.486×10-4 (~1
1800 𝑢) 0.511
The nucleus is about 100,000 times smaller than the atom
After the gold foil experiment, Rutherford measured the radius of the nucleus as
10−14 𝑚
He conducted scattering experiments to find this result
The actual size of a nucleus is 10−15 𝑚21, a femtometer
It takes its name from Italian Enrico Fermi
The electron cloud has a radius of 10−10 𝑚
If an atom were a football stadium, the nucleus would be a marble22
The equation 𝑟 ≈ 𝑟0𝐴1/3 relates atomic radius to atomic weight
𝑟0 = 1.2 × 10−15 𝑚
Nuclei have volume proportional to A
Hence, all nuclei have the same density
Isotopes
Isotopes of an atom have equal numbers of protons but differing numbers of neutrons
In Greek, “isotope” roughly means “the same place”
20
21
22
All isotopes of an element occupy the same spot on the periodic table
Isotopes have similar chemical properties
Neutrons do not usually affect chemical bonding
They have very different nuclear properties, especially those of stability and abundance
Isotope of Hydrogen Symbol Abundance Stability
Plain = hydrogen 𝐻11 99.99% Stable
Deuterium 𝐻12 Very little Stable
Tritium 𝐻13 Very little Radioactive (unstable)
Scientists create isotopes by bombarding nuclei with alpha particles, neutrons, or other
nuclei
All isotopes heavier than Californium23 (z = 98) can only be created artificially
Nuclear Forces
The strong nuclear force2425 holds protons and neutrons together in the nucleus
This force only acts over very short ranges
The binding energy is the energy needed to split apart the nucleus
The total mass of a nucleus’s components exceeds that of the nucleus26
The extra mass comes from the binding energy
𝐻𝑒24 has an unusually high binding energy, affecting its decay properties
Elements 𝐻𝑒24 = 2 × 𝑛0
1 + 2 × 𝑝+11
Mass 4.001506 𝑢 ≠ 2 × 1.008665 𝑢 + 2 × 1.007276 𝑢
Sum: 4.001506 𝑢 ≠ Sum: 4.031882 u
Difference 0.03076 u = 28.3 MeV, 7 MeV/nucleon
A nucleus’s binding energy relates to its nuclear stability
Neutrons increase nuclear stability by not repelling protons
𝒁 Stability properties
≈56 High stability - highest binding energies, e.g. iron, nickel
>60 Binding energies decrease with atomic number
Larger nuclei have weak short-range nuclear forces
>20 Require many more neutrons than protons to remain stable
> 83 No number of neutrons can stabilize the nucleus
Quantum effects also contribute to nuclear stability
Nuclei with even numbers of neutrons are more stable
If the number of neutrons or the number of protons is a magic number, the nucleus
is unusually stable
23
24
25
26
The magic numbers are 2, 8, 20, 28, 50, 82, and 12627
Helium-4 and oxygen-16 are doubly magic
In 1949, Maria Goeppert Mayer and Eugene Wigner designed a “shell” model
This model of nucleons explained the presence of magic numbers
The magic numbers equal the protons and neutrons needed to fill each shell
Neutrons and protons are fermions and so follow the Pauli exclusion principle
Protons and neutrons are fermions because they have half-integer spin
When the number of protons or neutrons is even, the spins cancel out
Particles of opposing spin align to decrease energy
Nuclei with uneven numbers of protons or neutrons have a magnetic moment
A nucleus with a magnetic moment will respond to an external magnetic field
Aligning the magnetic moment with the field decreases the nucleus’s energy
An oscillating magnetic field can cause the nucleus to rapidly oscillate between two
energy levels
Magnetic resonance imaging (MRI)28 uses a strong magnet to align all of the
hydrogen-1 atoms in a body
Radio waves target specific areas and break the alignment of hydrogen nuclei
Without the radio waves, the nuclei fall back and release energy
MRI does not damage cells, but still provides high resolution images
Radioactivity The discovery of radioactivity
In 1895, German physicist Wilhelm Roentgen made the first observation of x-rays
He experimented with a cathode ray tube
The rays passed through cloth, paper, and books to cause a view-screen to glow
He called them “X” rays since they were then unknown
Roentgen won the 1901 Nobel Prize for this discovery
French physicist Henri Becquerel discovered spontaneous radiation later that year
He observed it in uranium salts that behaved similar to Roentgen’s x-rays
Radioactivity refers to spontaneous radiation
Radioactive isotopes spontaneously emit radiation and
In the process, they transform into other isotopes
Marie Curie measured the radioactivity of many substances
She built on her husband Pierre Curie‘s work on crystals
She analyzed pitchblende and torbernite
These minerals that contain uranium
Their radioactivity was proportional to the quantity of uranium
Hence, a change in uranium’s atomic structure induced radiation
In 1898, the Curies discovered polonium and then radium
They named polonium after Marie’s home country Poland29
The Curies and Becquerel jointly won the 1903 Nobel Prize in Physics
Marie Curie also won the 1911 Nobel Prize in Chemistry
27
28
29
She is the only person ever to win two Nobel Prizes
Heavy exposure to radiation ruined Marie’s health
She lost most of her sight in the 1930s and died in 1934 of aplastic anemia
Her original notes are too radioactive to be handled without shielding30
Radioactive decay
In 1900, Ernest Rutherford and Frederick Soddy identified the three types of radiation:
alpha (α), beta (β), and gamma (γ)
They also suggested that radiation results from radioactive decay
During radioactive decay, unstable isotopes transform into stable isotopes
Charge and nucleons are always conserved
The parent nucleus X transforms into a daughter nucleus Y, except in gamma decay
Gamma decay involves a descent from a higher energy state X* to a lower energy
state X*
Type Alpha Beta minus Beta plus Gamma
Emits Helium nucleus Electron and
antineutrino
Positron and
neutrino Photon
Notation 𝑯𝒆𝟐𝟒 𝒆−
−𝟏𝟎 𝒆+
𝟏𝟎 𝜸
Decay
formula 𝑿𝒁
𝑨 → 𝑯𝒆𝟐𝟒 + 𝒀𝒁−𝟐
𝑨−𝟒 𝑿𝒁𝑨 → 𝒆−
−𝟏𝟎 + 𝒀𝒁+𝟏
𝑨 + �̅�𝟎𝟎 𝑿𝒁
𝑨 → 𝒆+𝟏𝟎 + 𝒀𝒁−𝟏
𝑨 + 𝒗𝟎𝟎 𝑿∗
𝒁𝑨 → 𝑿𝒁
𝑨
Example 𝑈92238 → 𝐻𝑒2
4 + 𝑇ℎ88234 𝑪𝟔
𝟏𝟒 → 𝒆− + 𝑵𝟕𝟏𝟒 + �̅� 𝑪𝟔
𝟏𝟐 ∗ → 𝑪𝟔𝟏𝟐 + 𝜸
During alpha decay, an atom releases an alpha particle
An alpha particle is two protons and two neutrons
It is the same as a helium nucleus
This particle’s high binding energy
makes it energetically favorable for
decay
Emitting 2 neutrons and 2 protons
individually is not energetically
favorable
Eg: 𝑋𝑍𝐴 → 𝑛0
1 + 𝑛01 + 𝑝1
1 + 𝑝11 + 𝑌𝑍−2
𝐴−4
Alpha decay occurs in elements at least
as heavy as tellurium (𝑍 ≥ 52)
Radioactive nuclides release alpha
particles at 5% of the speed of light
Alpha particles lose energy quickly due
to their high mass
They usually stop in a few centimeters
During beta decay, an atom releases either an electron or positron
A positron is electron’s antiparticle – an electron with a positive charge
Scientists only discovered beta plus decay decades after beta minus decay
The positron lasts for 10−10 seconds in a vacuum before annihilating with an
electron
30
Beta minus particles come from the nucleus, not the surrounding electron cloud
A neutron in the nucleus transforms into a proton and an electron
𝑛01 → 𝑝+
11 + 𝑒−
−10
Free neutrons outside the nucleus perform such decay in 15 minutes
In the 1920s, physicists including Neils Bohr realized that conservation of energy, spin,
and angular momentum did not occur in beta decay
In 1930, Wolfgang Pauli hypothesized another particle in beta decay
Enrico Fermi called this particle a neutrino, or “little neutral one”
The neutrino was first observed in 1950
Properties of the Neutrino
Neutrally charged Fermion with half-integer spin
Essentially massless Weakly interacts with matter
Released by nuclei in electron capture (K-capture):
• The nucleus absorbs an electron from the K energy level of its electron cloud
• Higher energy electron drops down to fill the shell, releasing an X-ray photon
• A proton combines with the electron in the nucleus to produce a nucleus and a neutrino
• The nucleus releases the neutrino
• Example: 𝐵𝑒47 + 𝑒− → 𝐿𝑖3
7 + 𝜈
During gamma decay, an atom releases electromagnetic radiation, or photons
Gamma decay often proceeds after alpha or beta decay produces an excited nucleus
Photons produced by nuclear transitions differ from those in electron transitions
Nuclear transition photon Electron transition photon
Gamma rays X-rays
Millions of eV Tens of eV
Scientists can create unstable isotopes that do not exist naturally
In 1934, Irene Joliot-Curie and Frederick Curie artificially synthesized a radioactive
isotope of phosphorous
Irene was the daughter of Marie and Pierre Curie
They fired alpha particles at aluminum
𝐻𝑒24 + 𝐴𝑙13
27 → 𝑃1530 + 𝑛; 0
1 𝑃1530 → 𝑆𝑖14
30 + 𝑒+
Together they won the 1935 Nobel Prize in Chemistry
Medically useful isotopes are produced artificially
Over 3,000 radioactive isotopes have been synthesized
The math of decay
The timing of decay cannot be predicted for a specific nucleus31
For a group of radioactive atoms, decay happens exponentially
The number of decays is proportional to the number of nuclei present and to the time
that has elapsed
The rate of decay has a similar exponential relation
31
Decay Laws
𝚫𝑵 = −𝝀𝑵𝚫𝒕 𝑵 = 𝑵𝟎𝒆−𝝀𝒕 𝑹 = 𝑹𝟎𝒆−𝝀𝒕
Δ𝑁 = number of decays in a period of time 𝑁 = number of nuclei present at a given time
𝑁0 = initial nucleus population 𝑅 = decay rate at a given time
t= time elapsed Δ𝑡 = a period of time
𝑅0 = initial decay rate 𝜆 = decay constant
The decay rate is measured in Curies or Becquerels
1 Ci (Curie) = 3.7 × 1010 𝑑𝑒𝑐𝑎𝑦𝑠/𝑠
1 Bq (Becquerel) 1 𝑑𝑒𝑐𝑎𝑦/𝑠
The Becquerel became the standard unit for decay rate in 1975
The half-life of an isotope measures the time for half a sample of that isotope to decay
Half-life equation
𝑻𝑯 =𝐥𝐧 𝟐
𝝀=
𝟎. 𝟔𝟗𝟑
𝝀
Examples: Hydrogen-4 10−22 seconds
Tellurium-12 1024 years
Isotopes with a long half-life have a more stable nucleus
In any decay, a set of particles moves from a state with high potential energy to a state
with lower potential energy
The mass of products will always be less than the mass of the original particles
The potential energy difference comes from the mass difference
Quantum mechanics explains why decay is probabilistic
An alpha particle in a nucleus has a wave function
The nuclear and Coulombic forces contain the alpha particle in a potential barrier
The potential barrier has a size proportional to the nucleus’s size and charge
Much like quantum tunneling, the alpha particle can escape the confining forces
If the potential barrier is small, the alpha particle will escape more easily
This isotope would have a short half life
Decay chains
A decay chain occurs when the daughter nucleus is also radioactive
Each decay step has its own half-life
The three primary decay chains in nature occur in thorium, uranium, and actinium
Neptunium’s decay chain does not occur in nature
A chain starts with a heavy long-life isotope and ends with a stable isotope of lead
In thorium-232’s chain, bismuth-212 performs either alpha or beta minus decay
Decay chains explain why short-lived isotopes still exist in nature
Radium-226 has a half-life of 1,600 years
The Solar System has existed for 4.6 billion years
All original radium-226 has decayed
Uranium-238’s decay chain replenishes the isotope
Uranium-238 has a half-life of 4.47 × 109 years
Detecting Radioactivity
Dosage measures the quantity of radiation an object receives
The standard unit of dosage is the Sievert (Sv)
One Sievert equals the effect of radiation that puts 1 Joule into 1 kg of tissue
The United States uses the rem, equal to 0.01 Sieverts
All methods of detecting radiation measure radiation’s ionizing effects
Radiation ionizes atoms by removing electrons
Geiger counter Scintillation counter Proportional counter
Invented by Hans Geiger32
Contain positively charged
wire surrounded by tube of
inert gas
Use scintillating material
instead of gas
Provide information about the
energy level of the radiation
Measure energy of incoming
radiation
Essentially complex Geiger
counters
Radiation ionizes gas
atoms, releasing electrons
Radiation excites the crystal,
usually NaI
Incoming radiation trigger an
"avalanche" of ions
Electrons jump to wire and
trigger electric pulse
Excited crystal falls back to its
ground state and releases a
photon
Ions move towards a high-
voltage wire, changing its
current
Electric pulse produces
clicking sound
Photomultiplier tube converts
photon to electric pulse
Change is proportional to
particle energy
American Donald Glaser invented the bubble chamber in 1952
It and its counterpart, cloud chambers, track the path of radiation
The path provides information on the particle’s mass, charge, and momentum
Positive and negative particles curve in opposite directions
Cloud chamber Bubble chamber
Medium Vaporized water or alcohol Heated liquid hydrogen
Result
Particles are ionized. Pressure
condenses vapor around the
ions, forming trails
Pressure is decreased; particle
in an electric or magnetic field
leaves behind a trail of bubbles
Practical Applications of Radiation Sources of Radiation
The average American receives 6.2 mSv of background radiation every year
Half of this radiation comes from man-made sources, mostly x-ray procedures
One x-ray delivers 0.02 mSv to the body
Less than 0.1% comes from the nuclear industry
The other half comes from natural sources33
32
33
Cosmic rays Radon-222 Other sources
High energy particles from
beyond the solar system
Mostly free protons
Shielded by the atmosphere
More prominent in high altitude
areas
>Ex: Denver receives 2x more
radiation than sea level
>Affects pilots' annual
permitted dosages 34
Largest source of natural
background radiation
Found in decay chain of
uranium-238
Accumulates in basements
as a dense gas
Second most frequent
cause of lung cancer after
smoking
Can be tested for with
detection kits35
Radioactive
minerals
Radioactive
nuclei in food
Potassium-40 -
results in 0.4 mSv
per year
Health Effects of Radiation36
Ionizing radiation has enough energy to excite electrons
Both ionizing and non-ionizing radiation can thermally excite atoms, causing burns
Non-ionizing radiation
𝐸𝑛𝑒𝑟𝑔𝑦 < 10 − 33 𝑒𝑉
Radio waves
Microwaves
Infrared, visible, sun light
Ionizing radiation
𝐸𝑛𝑒𝑟𝑔𝑦 > 10 − 33 𝑒𝑉
X-rays and gamma-rays
High energy UV light
Decay emissions
Ionizing radiation damages living things when it strikes a molecule in the body
An electron is removed, creating an ion or free radical3738 (neutral molecules with
unpaired electrons)
The free radical react with other elements to produce irregular compounds
Cells repair weak radiation damage only slowly
However, the body cannot regenerate nerve cells
Damage to DNA can lead to mutations, causing genetic disorders or cancer
Overexposure to UV radiation causes sunburns, which can damage skin cells’ DNA
Dead skin cells peel off
Some forms of radiation are more dangerous than others
34
35
36
37
38
Gamma rays Most destructive form
Travel farthest into matter
Alpha particles Blocked by skin
Highly damaging if alpha emitter is consumed39
Neutrinos
Interact weakly with matter
Do not affect human health
Strike earth from sun with flux of 1011 neutrinos / cm2
Radiometric Dating
Radiometric dating uses decay rates to calculate a material’s age
The most common form is carbon dating
In the 1940s, American Willard Libby developed carbon dating
He won the1960 Nobel Prize in Chemistry
Carbon-12 and carbon-13 are stable, but carbon-14 undergoes beta decay
Carbon-14 transforms into nitrogen-14 with a half-life of 5,730 years
Carbon dating only works with objects less than 50,000-years old
Older materials have an undetectable carbon-14 concentration
Process of carbon dating
Cosmic rays produce free neutrons in the atmosphere
Free neutrons combine with nitrogen-14 to form carbon-14, which has a
natural abundance of 1 per trillion in living organisms and the atmosphere
Living organisms take in carbon dioxide in respiration
The organism dies, and carbon-14 in its body decays
Ratio of carbon-14 to carbon-12 decreases with time
Scientists measure the ratio to determine the organism’s age
Fluctuations in the atmosphere’s carbon-14 concentration limit carbon dating’s accuracy
Varying intensities of the Earth’s and Sun’s magnetic fields alter the strength of
incoming cosmic rays
Oceans hold carbon-14 as dissolved carbon dioxide
Inconsistent ocean temperatures alter the rate at which carbon flows into the
atmosphere
Uranium dating works on objects older than 50,000 years
Uranium-238 is used instead of carbon-14
This isotope has a half-life of 4.5 × 109 years
The technique revealed that the oldest moon rocks and the oldest Earth rocks have
the same age
The moon was probably formed out of the Earth in a primordial collision
Uranium dating and argon-argon dating40 have recreated the fossil records
39
40
Geologists date the rock layers in which fossils are found
Primordial isotopes like uranium-238 were present in Earth’s crust at its formation
Earth’s age is 4.5 × 109 years
For a primordial isotope to be detectable its half-life must be > 5 × 107 years
Industrial applications
Radiation therapy destroys cancer cells’ DNA with ionizing radiation
Without DNA, the cancer cells die
The radiation must precisely kill only the cancerous cells
Multiple low intensity beams intersect at the location of the cancerous cells41
Gamma rays are most commonly used for cancer therapy
Beta radiation is used to kill skin cancer and tumors close to the skin
Radiation sterilization was first used in the mid-twentieth century
Gamma rays are commonly used, generally using cobalt-60 as the emitter
Eggs, grains, fruits, and vegetables can be sterilized without becoming radioactive
It may chemically alter the food’s taste and nutrition
The United States Food and Drug Administration regulates food irradiation
Smoke detectors contain under 1 microgram of radioactive americium-241
Americium-241 transforms into neptunium-237 in alpha decay
The alpha particles produce a current in the detector
Smoke absorbs the alpha particles, breaking the current
Radioactive tracers use isotopes to create an observable path through a system
Uses of radioactive tracers
Medicine
• Doctors42 prepare sodium iodide with radioactive iodine-131
instead of iodine-127
• The patient ingests the harmless sodium iodide
• The radioactive iodide collects at the patient's thyroid glands,
providing a measure of thyroid health
• Doctors can then detect hemorrhage or tumor formation
Agriculture
• A radioactive solution is injected into a plant’s root system
• The solution’s uptake throughout the plant is measured
• Scientists can then detect information about the plant’s
fertilizer or other chemical use
Auto mechanics
• The engine's cylinder walls are coated with a tracer
• The engine is operated for some time
• The tracer's concentration in the lubricating oil is analyzed
41
42
Nuclear Reactions A brief history
Two nuclei collide and form another nucleus
in a nuclear reaction
Ernest Rutherford induced a nuclear reaction
when he discovered the proton in 1917
He was scattering alpha particles from
nitrogen gas
He induced the reaction: 𝐻𝑒24 + 𝑁7
14 →𝑂8
17 + 𝐻11
Unfortunately, Rutherford did not
understand the nuclear changes
occurring43
In 1932, Irish physicist Ernest Walton and British physicist John Cockcroft became known
as the first men to “split the atom”
They performed the reaction 𝑝11 + 𝐿𝑖3
7 → 2 × 𝐻𝑒24
Like chemical reactions, compounds react to form new compounds
However, nuclear reactions release energy in the order of MeVs rather than eVs
Mass-energy conversion Fusion Fission Direct
Involves light nuclei heavy nuclei particle-antiparticle pairs
% mass converted 0.7% 0.1% 100%
Particle accelerators now collide particles with tremendous amounts of energy
The Large44 Hadron Collider accelerates protons to 99.9999% of the speed of light
These protons have 1 TeV45 of energy
The LHC is located at CERN, a research facility in Europe
A reaction’s Q value measures its energy output or input
43
44
45
Reaction Exothermic: Q > 0 Endothermic: Q < 0
Energy Released as kinetic energy of products
and gamma rays
Requires input - kinetic energy of
reactants
Example 𝐻12 + 𝐿𝑖3
6 → 𝐻𝑒24 + 𝐻𝑒2
4 𝐻𝑒24 + 𝑁7
14 → 𝑂817 + 𝐻1
1
Mass of
reactants
2.014101 𝑢 ( 𝐻12 ) + 6.015123 𝑢 ( 𝐿𝑖3
6 )
= 8.029224 𝑢
4.002603 𝑢 ( 𝐻𝑒24 ) + 14.003704 𝑢 ( 𝑁7
14 )
= 18.005677 𝑢
Mass of
products
4.002603 𝑢 ( 𝐻𝑒24 ) + 4.002603 𝑢 ( 𝐻𝑒2
4 )
= 8.005206 𝑢
16.999132 𝑢 ( 𝑂817 ) + 1.007825 𝑢 ( 𝐻1
1 )
= 18.006957 𝑢
Net energy 0.024018 𝑢 = 22.4 𝑀𝑒𝑉 −0.001280 𝑢 = −1.19 𝑀𝑒𝑉
Produces 22.4 MeV Requires a little more than 1.19 MeV
Actual energy input slightly exceeds the Q value in endothermic reactions
The Q value energy produces the product particles at rest
To maintain conservation of momentum, the products must have kinetic energy
Required kinetic energy, 𝑲𝑬𝒎𝒊𝒏 = (𝟏 +𝒎
𝑴) |𝑸|
𝐾𝐸𝑚𝑖𝑛 = threshold energy 𝑀 = mass of stationary nucleus
𝑚 = mass of incoming nucleus 𝑄 = Q value of reaction
E.g.: reaction with 𝐻𝑒24 and 𝑁7
14 → minimum energy = 1.53 MeV
Fission reactions
In nuclear fission, a massive nucleus releases energy and splits into fission products
Most of the time, the heavy nucleus first collides with another particle
In rare cases, nuclear fission occurs spontaneously
Fission releases up to 100 MeV of energy per reaction
Fission products, or fission fragments, are lighter nuclei released in nuclear fission
These have a high neutron to proton ratio
Neutrons stabilize protons in heavy nuclei
“Neutron heavy” fission products decay further into even lighter nuclei46
Types of
nuclei
Fissile Fertile Neither
Performs fission after colliding
with a slow particle with
energy < 1 𝑀𝑒𝑉
Performs fission after colliding
with a fast particle with energy
> 1 𝑀𝑒𝑉
Never performs
fission
English professor James Chadwick discovered the neutron in 1932
Earlier scientists created reactions by firing alpha particles or protons at nuclei
After 1932, they used mostly neutrons instead
The nucleus’s positive charge does not repel neutrons
Low energy neutrons can still penetrate the nucleus
This process is neutron bombardment
In the 1930s, Enrico Fermi created new elements with neutron bombardment
46
Uranium Neptunium Plutonium
𝑍 = 92 𝑍 = 93 𝑍 = 94
Heaviest known element at the time;
target of neutron bombardment
New elements synthesized by
neutron bombardment
In 1938, German physicists Otto Hahn and Fritz Strassman noticed that nuclei tend to
split in two after neutron bombardment
The two pieces were each around half as massive as the target nucleus
Ex: Barium is half as massive as uranium
The existing theory behind decay did not explain this phenomenon
Lise Meitner and Otto Robert Frisch explained this observation using the liquid drop
model of the nucleus
According to this model, heavy nuclei oscillate and split in half
Otto Frisch first used the term “fission”
He was alluding to how living cells split apart in biological fission
Neils Bohr realized that the energy released in nuclear fission could be harnessed
He visited the United States and worked with John Wheeler and Enrico Fermi
In a chain reaction, a fission reaction sparks more reactions in neighboring nuclei
Before the 1930s, scientists only knew of chemical chain reactions
The finding proved a nuclear chain reaction to be theoretically possible
In 1933, Hungarian Leo Szilard envisioned the self-sustaining nuclear reaction
The reaction had to be triggered by a neutron and release at least one neutron
The multiplication factor k measures the average number of released neutrons which
will trigger another fission
Some neutrons are captured without fission, and others escape the system
Subcritical: 𝑲 < 𝟏 Critical: 𝑲 = 𝟏 Supercritical: 𝑲 > 𝟏
Number of reactions
decreases with time
Constant number of reactions →
constant power generated
Increasing number of
reactions over time
Cannot sustain decay
chains Optimal for power generation
Optimal for nuclear
weapons
Calculating energy per reaction from binding energies of nucleons
Ex: 235 nucleons → 3.2 × 10−11 𝐽 = 200 𝑀𝑒𝑉 = 235 ∗ (8.5 𝑀𝑒𝑉 − 7.6 𝑀𝑒𝑉)
Binding energy of nucleons Reactants: 7.6 𝑀𝑒𝑉 Products: 8.5 𝑀𝑒𝑉
Energy density Gasoline: 4.4 × 104 𝐽 Uranium: 8.8 × 1010 𝐽
The first nuclear chain reaction was observed in uranium-235
Uranium-235 can follow many decay paths
It is the only isotope useful for nuclear power generation
Uranium-238 absorbs neutrons without performing fission
It forms 95% of all uranium, while uranium-235 constitutes 0.7%
Uranium-235 releases 2.5 neutrons per decay
Enriching uranium increases the concentration of useful uranium-235
Two possible Uranium-235 decay chains
𝒏𝟎𝟏 + 𝑼𝟗𝟐
𝟐𝟑𝟓 → 𝑩𝒂𝟓𝟔𝟏𝟒𝟏 + 𝑲𝒓𝟑𝟔
𝟗𝟐 + 𝟑 𝒏𝟎𝟏 Most common; produces barium and krypton
𝒏𝟎𝟏 + 𝑼𝟗𝟐
𝟐𝟑𝟓 → 𝑿𝒆𝟓𝟒𝟏𝟒𝟎 + 𝑺𝒓𝟑𝟖
𝟗𝟒 + 𝟐 𝒏𝟎𝟏 Less common; produces xenon and strontium
Uranium enrichment
Power plants 3-4% uranium-235 → critical nuclear reactions
Weapons-grade 90% uranium-235 → supercritical nuclear reactions
Methods of uranium enrichment
Gas diffusion
(Early method)
• Uranium + fluorine →𝑈𝐹6 gas
• Lighter uranium-235 has a higher velocity at uniform temperatures
• Faster uranium-235 diffuses more quickly through a membrane
Magnetic separation
(Early method)
• Uranium ions enter a magnetic field
• The magnetic field bends the paths of the ions
• Lighter ions follow a more curved path
Gas centrifuge
(Modern method)
• Uranium hexafluoride gas is spun in a cylinder
• Heaver ions flow to outer edge
• Uranium-235 collects inside
Laser enrichment
(Experimental)
• A stream of ions passes in front of a laser
• The laser accurately strikes lighter ions, shifting their paths47
• Little energy is spent
Fundamentals of fusion
In nuclear fusion, two smaller nuclei collide and form a larger nucleus
Light nuclei conducting fusion Heavy nuclei conducting fusion
Mass of reactants > mass of product
Energy is released
Mass of product > mass of reactants
Energy must be input
Example: Deuterium and tritium fuse into helium - 𝐻13 + 𝐻1
2 → 𝐻𝑒24 + 𝑛0
1
Mass of reactants: Mass of products:
2.013553 𝑢 ( 𝐻12 ) + 3.015501 𝑢 ( 𝐻1
3 )
= 5.029054 𝑢
4.001506 𝑢 ( 𝐻𝑒24 ) + 1.008665 𝑢 ( 𝑛0
1 )
= 5.010171 𝑢
Mass of products – mass of reactants = −0.018883 𝑢 = −17.59 𝑀𝑒𝑉
Electric forces between nuclei create a barrier to fusion called the Coulomb barrier
Two nuclei brought very close together have an attractive nuclear force that overcomes
the Coulomb barrier
Quantum tunneling explains nuclei’s ability to cross the Coulomb barrier
Colliding nuclei have temperatures near 107 K
In thermonuclear fusion, nuclei collide and form tightly bound nuclei
47
Like chemical combustion, it requires high temperatures to initiate
Continuous energy releases sustain both types of reaction
Products have less mass, and energy is output
Stellar fusion produces energy in stars
Their cores are fusion reactors operating at millions of degrees
Young stars perform hydrogen fusion, while old stars perform helium fusion
1920 English physicist Arthur Eddington proposed that stars produce
energy by combining hydrogen into helium
1934 Australian Mark Oliphant and Ernest Rutherford collide two
deuterium nuclei to form helium
1939 Hans Bethe describes the proton-proton chain and the carbon-
nitrogen-oxygen cycle
1967 Hans Bethe wins the Nobel Prize for describing stellar fusion
The Sun converts 657 million tons of hydrogen into 653 million tons of helium per day
The Sun is 74% hydrogen and 25% helium by mass
4 tons of energy is released as radiation, light, and the solar wind48
The solar wind is a stream of light particles ejected during fusion
A star’s gravity provides the energy for thermonuclear fusion
Fusion energy generates pressure outwards
Stars need to be hot and dense enough for fusion reactions to occur
Light stars conduct a fusion process called the proton-proton chain
The Proton-Proton Chain
Reaction Energy Output
2 × ( 𝐻11 + 𝐻1
1 → 𝐻12 + 𝑒+ + 𝑣) 𝑄 = 2 × (0.42 𝑀𝑒𝑉)
2 × ( 𝐻11 + 𝐻1
2 → 𝐻𝑒23 + 𝛾) 𝑄 = 2 × (5.49 𝑀𝑒𝑉)
𝐻𝑒23 + 𝐻𝑒2
3 → 𝐻𝑒24 + 𝐻1
1 + 𝐻11 𝑄 = 12.86 𝑀𝑒𝑉
Total 4 𝐻11 → 𝐻𝑒2
4 + 2𝑣 + 2𝛾 + 2𝑒+ 𝑄 = 24.68 𝑀𝑒𝑉
Positrons release more energy after colliding with electrons
2 × (𝑒+ + 𝑒− → 𝑄); 𝑄 = 2 × (0.511 𝑀𝑒𝑉) = 1.02 𝑀𝑒𝑉
The slowest first step acts as a bottleneck
It regulated the conversion rate
Heavier stars follow a different process, the carbon cycle (CNO cycle)
The CNO cycle converts hydrogen to helium, with no net carbon change
CNO stands for carbon-nitrogen-oxygen, the intermediate elements
Applications Nuclear reactors
Nuclear reactors harvest energy from sustained chain reactions
48
Reactors must control the reaction rate
One kilogram of uranium-235 provides
the same energy as 20,000 tons of TNT
In a reactor, the moderator slows down
emitted neutrons
The neutrons emitted by reactions
have very high kinetic energies around
2 MeV
Uranium-235 does not easily
absorb fast neutrons
Slow neutrons conduct fission with
uranium-235
Uranium-238 does not absorb slow
neutrons
A good moderator absorbs much of the neutron’s energy
The moderator should have nearly the same mass as the neutron
Moderators with different masses absorb little energy
Imagine a ping pong ball bouncing off a billiard ball49
Moderators
Hydrogen, 𝑯𝟏 Deuterium, 𝑯𝟐 Graphite, 𝑪𝟏𝟐
Theoretically is the best moderator
but in practice absorbs neutrons to
form deuterium
Does not slow neutrons effectively
Slows neutrons without
absorbing them
Is found in heavy water,
replacing hydrogen-1
Is used in first
nuclear reactor
Slows neutrons after
100 collisions
Control rods50
Maintain reactor’s criticality; contain neutron-absorbing boron
Reactor startup, K > 1 Reactor operation, K =1 Reactor shutdown, K <1
Rods retracted Rods control reaction rate Rods inserted
Enrico Fermi created the first nuclear reactor on December 2nd, 1942
He constructed it on the University of Chicago’s racquet courts51
A pile of graphite bricks surrounded the uranium fuel
Cadmium control rods penetrated the reactor core52
A concrete containment chamber surrounds the steel reactor vessel
The vessel contains the core, which holds fuel surrounded by a moderator
Modern reactors use water for the moderator
The fuel usually contains 2-4% uranium-235 and 96-98% uranium-238
Most reactors are a type of light water reactor
49
50
51
52
Light water reactors Heavy water reactors
Boiling water Pressurized water
Loop of water both
cools reactor and
powers steam turbine
Pressurized cooling loop transfers
energy to a secondary loop which
generates steam
Radioactive coolant does not enter
steam turbine
Heavy water moderates
neutrons extremely well
Can induce reactions in
unenriched fuel
Employs relatively
simple design Common in United States
Common in Canadian reactors
More expensive
Coolant flows through the core and absorbs thermal energy
Most reactors use water
A few use liquid sodium
Coolant exiting the reactor boils water to produce steam
The steam generates electricity by powering a conventional steam turbine
Nuclear reactors have many applications
They can generate electricity, including to power ships and submarines
They also generate neutrons for research, medical, and industrial use
Nuclear reactors generate a significant portion of the world’s energy needs
1951 EBR-153 reactor in Arco, Idaho generates electricity for four light bulbs
1954 Soviet Union connects a nuclear reactor to the power grid
2012 Nuclear power generates 10.9% of the world’s energy
2015 438 reactors operate in 30 countries
Breeder reactors
Plutonium-239 is useful for nuclear fuels and nuclear weapons
Plutonium-239 is not a fission product, but rather forms from uranium-238
Origins of Plutonium-239
Uranium-238 absorbs a neutron without reacting 𝑈238 + 𝑛1 → 𝑈239
Uranium 239 has a half-life of 23.5 minutes before
decaying into neptunium-239 𝑈239 → 𝛽−1
0 + 𝑁𝑝239
Neptunium-239 performs a second beta decay 𝑁𝑝239 → 𝛽−10 + 𝑃𝑢239
Breeder reactors generate plutonium-239
In World War II, they produced plutonium for nuclear weapons
53
Less effective moderators increase the number of neutrons in the reactor
Liquid sodium leaves neutrons with high kinetic energy
These neutrons react with uranium-238 to form plutonium-239
Some breeder reactors generate more fuel than they consume
Breeder reactors have decreased since the 1980s and halted in the United States
There is nothing wrong with the uranium fuel supply
It has not been substantially depleted
However, breeder reactors produce the fuel for nuclear weapons
Governments fear the proliferation of weapons-grade nuclear fuel
In addition, breeders are expensive and complex
Nuclear power challenges
Nuclear reactors produce hazardous radioactive wastes54
Some wastes have very long half-lives and stay hazardous for a long time
Plutonium-239 has a half-life of 24,000 years
These wastes must be contained safely as long as they remain dangerous
Some fission products decay away quickly and can be stored temporarily
Nuclear reactors must be decommissioned after 30 years of operation
Radioactivity builds up on the reactors components
Structural materials degrade after prolonged exposure to ionizing radiation
Old reactors must be completely dismantled and radioactive materials removed
This process is very expensive
Nuclear reactors still hold many advantages over coal, oil, and natural gas plants55
Coal power plants release many greenhouse gases and expose workers to radon
Nuclear power plants only release water vapor, which converts to snow and rain
Nuclear plants release very little radiation, an average of 0.1 mSv per year
This amount equals 0.003% of the average annual background radiation
It also constitutes 1
200 the radiation from one chest x-ray
The United States produced 1/3 of the world’s nuclear energy in 2013
Nuclear power provided 19.5% of the country’s energy in 2014
In contrast, France generates 75% of its electricity through nuclear plants
No new plants have been developed in the United States since the 1970s
Political and economic forces have halted the building of new power plants
Although the risk from nuclear power plants is small, accidents are high-profile and
alarming
Nuclear power plants are very expensive to build
The United States still builds new reactors to add to existing plants
Accidents can be meltdowns or explosions
In meltdowns, the nuclear fuel overheats and melts through its containment
Explosions occur due to over-pressurized coolant
The Three Mile Island5657 incident occurred on March 29, 1979 in Pennsylvania
54
55
56
57
Three Mile Island Accident
Water pump shuts down
Secondary coolant loop stops circulating
Reactor shuts down but still generates heat
Secondary loop boils off, leaving only primary loop
Primary loop overheats and overpressurizes
Water floods the containment structure and is pumped outside
Though it was the worst accident in United States history, it had no impact on public
health
The Chernobyl incident occurred on April 26th, 1986 in the former Soviet Union
This was the worst nuclear accident in history
A sudden power surge ruptured the reactor vessel, causing a large explosion
Its radioactive cloud had 400 times more radiation than the Hiroshima bomb
Thirty people died and hundreds of thousands had to evacuate58
Such a disaster could not occur in the United States, as it uses different plant designs
On March 11th, 2011, the Fukushima Daiichi nuclear accident occurred in Japan
It stands as the worst accident since Chernobyl
Fukushima Daiichi Nuclear Accident
9.0 earthquake forces reactor to shut down
Control rods drop down into the core
Cooling reactors need supply of coolant
Tsunami cuts power to the primary and secondary coolant pumps
Reactors melt down and explode
500,000 residents evacuated
A 2013 report finds that evacuated civilians suffered no health effects
All 54 Japanese nuclear plants shut down
Generation IV reactors will be constructed from 2030
These reactors minimize waste, increase safety, and impede nuclear proliferation
Nuclear weapons
Weapons research drove nuclear science in the 1940s
Nuclear weapons release nuclear energy rapidly in supercritical (K >1) reactions
They release energy on the order of 1 to 500,000 tons of TNT
The critical mass refers to the minimum mass of fissile fuel in a nuclear weapon59
In uranium-235, the critical mass forms a 6.8 cm diameter sphere
The Nagasaki bomb used another common fuel, plutonium-239
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59
Below the critical mass At the critical mass Above the critical mass
Neutrons escape fuel before
colliding with a nucleus
Every fission causes one more
fission
The reaction rate increases
exponentially
Nuclear fuel remains below critical mass until detonation
At detonation, conventional explosives bring the pieces together
Early weapons used a gun-type design
An explosive fires half of the mass at the other down a barrel
Modern implosion-type weapons use a sphere of explosives to compress the fuel
Applications of fusion
Thermonuclear weapons and hydrogen bombs release energy in nuclear fusion
The fusion bomb originated in the Manhattan Project
Hungarian Edward Teller suggested a fission bomb could trigger a fusion bomb
In 1951, Teller and Stanislaw Ulam designed a fusion bomb
Teller became known as the “father of the hydrogen bomb”
The first fusion bomb detonated in 1952, using Teller’s multistage design
Fission charges compress fission and fusion fuel, detonating the primary bomb
The primary stage compresses and detonates a secondary fusion bomb
It released 10.4 megatons of energy, 450 times more than the Nagasaki bomb
The largest hydrogen bomb ever built was the Tsar Bomba
The Soviet Union tested this weapon on October 30th, 1961
It had the same energy as 50 million tons of TNT60
Scientists have been trying to harness power from fusion reactions for 50 years
Potential fusion reactions for power generation must satisfy certain criteria
Criteria Components
(1) Must be exothermic
(2) Must conserve proton and
neutron number
(1) Light nuclei with minimal Coulombic repulsions
(2) Two reactants to maximize collision probability
(3) At least two products to conserve momentum
Fusion reactions with deuterium and tritium are candidates for power generation
However, hydrogen is optimal for use in nuclear fusion
It is the most plentiful element and all isotopes appear in water
Potential fusion reactions
Reaction 𝐻12 + 𝐻1
2 → 𝐻𝑒23 + 𝑛0
1 𝐻12 + 𝐻1
2 → 𝐻13 + 𝐻1
1 61 𝐻12 + 𝐻1
2 → 𝐻𝑒24 + 𝑛0
1
Energy output 𝑄 = 3.27 𝑀𝑒𝑉 𝑄 = 4.03 𝑀𝑒𝑉 𝑄 = 17.59 𝑀𝑒𝑉
Deuterium
1 gram in every 30 liters of sea water,
provides same energy as 10,000 liters
of gasoline
World’s deuterium supply contains
more energy than its fossil fuel plus
uranium supplies
Tritium Low natural abundance; half-life of
10 years
Synthesized by breeding lithium-6
𝐿𝑖36 + 𝑛0
1 → 𝐻13 + 𝐻𝑒2
4
60
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Fusion reactors have many advantages over fission reactors
Fusion reactors cannot melt down as the reaction cannot become supercritical
Reaction products are not used in subsequent reactions
Fusion produces no pollution or radioactive waste, only helium
Fusion energy requires extremely high temperatures
In the sun, fusion occurs at over 10 million K
These extremely high temperatures are the greatest barrier to fusion energy62
Fusion reactors must be self-sustaining at ignition, like fission reactors
The energy released by a reaction can power subsequent reactions
Scientists have not yet been able to achieve ignition
Reactors must compress nuclei to extremely high densities to increase reactions
Electrons separate from nuclei in atoms above their ionization energies
The cloud of positive nuclei and negative electrons forms a plasma
Most structural components would vaporize at these temperatures and densities
Lawson’s Criteria
Deuterium-tritium fusion Deuterium-deuterium fusion
𝑛𝜏 ≥1014𝑠
𝑐𝑚3 𝑛𝜏 ≥
1016𝑠
𝑐𝑚3
𝑛 = plasma ion density 𝜏 = plasma confinement time
In 1957, J.D. Lawson devised conditions for fusion power generation
Two methods exist for generating and sustaining fusion
In magnetic confinement, electromagnets trap high-temperature plasmas
A strong magnetic field bends the paths of ions in the plasma cloud
Magnetic confinement systems trap moving ions in a “magnetic bottle”
Tokamaks are toroidal containment devices with two magnetic fields
They trap the plasma in a ring shape
The Soviet Union developed the tokamak after World War II
Magnetic confinement aims to sustain nuclei at high temperatures
Inertial confinement fusion (ICF) systems use laser beams to compress atoms
A laser array compresses a target pellet containing deuterium and tritium
The pellet ionizes into a plasma
Less than 10−9 seconds later, the particle reaches 108 K and fusion occurs
ICF systems prevent nuclei from drifting apart by forcing them together quickly
The National Ignition Facility63 is the world’s largest ICF device
It lies in Lawrence Livermore National Laboratory in Livermore, California
The NIF targets a 2mm hydrogen pellet with the world’s most powerful laser
In 2012, the NIF shot a 500 trillion watt laser pulse
This pulse has 1,000 times more energy than the United States uses in an instant
At break-even, the energy output exceeds the energy needed to trigger fusion
Princeton’s Tokamak Fusion Test Reactor tried to achieve this point but failed
It heated plasma to over 200 million K, above hydrogen’s ignition temperature
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63
The TFTR operated from 1982 and shut down in 1997 after 15 years
The Joint European Torus (JET) is another tokamak design that operates today
The world’s largest experimental fusion system is the ITER in France
ITER originally stood for International Thermonuclear Experimental Reactor
The European Union, India, Japan, Korea, China, Russia, and the United States
collaborated on this project
ITER uses a magnetic confinement system, hoping to prove its feasibility
It will finish construction in 2027 and run deuterium-tritium fusion experiments
The Manhattan Project Background
In the decades after World War I, Italy and Germany fell under fascist rule
Italy’s Benito Mussolini and the Nazi Party’s Adolf Hitler led their respective countries
The two allied countries carried out racial discrimination and genocidal policies
Germany’s invasion of Poland in September 1939 started World War II
Enrico Fermi and Leo Szilard fled to the United States in 1939
Leo Szilard had first conceived of the nuclear chain reaction in 1933
He warned Franklin Delano Roosevelt that Germany might be researching nuclear
weapons
He proposed that the United States follow suit and also stockpile uranium
Szilard signed the letter with Einstein’s name to attract more attention
Einstein, a German-born Jew, also worried about Nazi Germany
When Hitler became chancellor in 1933, Einstein chose to stay in the United States
Einstein was a pacifist and opposed creating nuclear weapons
He shared Szilard’s concern about German research into nuclear weapons
In response to Szilard’s letter, Roosevelt created the Advisory Committee on Uranium
National Bureau of Standards director Lyman Briggs chaired the committee
It had the task of recommending how to proceed with nuclear research
On November 1, 1939, it reported that the United States should support Fermi and
Szilard’s research in chain reactions
The United States purchased $6,000 of uranium oxide and graphite64
At the time, Fermi believed that nuclear reactors were possible, but not bombs
Pilot research
Vannevar Bush pushed for research on nuclear weapons
Bush was a science administrator and president of the Carnegie Foundation
He could influence United States policy in his position
By 1940, he was concerned about German expansion
He noticed a lack of cooperation between researchers and the military
In June 1940, Bush became the chair of the National Defense Research Committee
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Roosevelt approved this committee in less than 15 minutes
This committee oversaw research and development of nuclear weapons
The S-1 subcommittee studied uranium enrichment
It included Ernest O. Lawrence, director of the Radiation Laboratory65 at the
University of California, Berkeley
He had invented the cyclotron, a particle accelerator and mass spectrometer
As a mass spectrometer, it could separate uranium-235 from uranium-238
The S-1 committee needed to produce a critical mass of uranium-235
Nobody knew if the critical mass was small enough to fit on a bomber
The committee explored gaseous diffusion, centrifuge separation, and
electromagnetic separation as enrichment methods
Simultaneously, Great Britain developed its own nuclear weapons program
They estimated the critical mass to be on the order of 10 kg
Its representative, physicist Mark Oliphant, visited the United States in August 1941
to help and assess the American program
He encouraged the American researchers by sharing British research with them
By 1941, the atomic bomb seemed to be possible
Roosevelt and his Vice President Henry Wallace met on October 9th, 1941 with
Vannevar Bush
Bush summarized the progress of American and British research
Roosevelt asked Bush to estimate the cost of an atom bomb
President Roosevelt wanted the US Army to manage bomb construction
Japan attacked Pearl Harbor on December 7th, 1941
The United States declared war on Japan the next day
Starting production
In March 1942, Bush informed Roosevelt that
Lawrence’s cyclotron had successfully refined uranium
He believed that a bomb would be complete by
1944
Roosevelt shared his concerns in a response (right)
In May 1942, Arthur Compton asked J Robert
Oppenheimer to perform calculations for the chain
reaction
Oppenheimer worked at the University of California,
Berkeley66
He formed a team with Hans Bethe, John Van Vleck, Edward Teller, Felix Bloch,
Emilio Segre, and Robert Serber
They found they needed double the amount of fission fuel previously estimated
However, they confirmed that a fission weapon could be built
In June 1942, the S-1 committee researched fuel enrichment
Vannevar Bush allocated $85 million for constructing enrichment plants
Three plants were built to enrich uranium, and one more for plutonium
The United States stockpiled uranium on Staten Island
It stored 12,000 tons of uranium ore from Colorado and Canada
65
66
“I think the whole thing
should be pushed not only in
regard to development, but
also with due regard to time.
This is very much of the
essence.” - FDR
Fermi created a chain reaction at the University of Chicago on December 2, 1942
The S-1 committee then finalized plans for bomb development
Roosevelt agreed to the proposals and allocated $500 million for the project
The Manhattan Project
The Army Corps of Engineers managed bomb production
On August 13, 1942, they set up an office in Manhattan, New York
The office became the Manhattan Engineer District, or The Manhattan Project
General Leslie R. Groves became the project’s director in September 1942
He came from the Army Corps of Engineers, where he had worked on the Pentagon
Groves drew criticism for his abrasive and critical personality
His focused, goal-oriented management helped the project meet crucial deadlines
Groves selected Oppenheimer as the leader of Project Y on July 20th, 1943
Project Y referred to the Manhattan Project’s weapons development lab
Ernest Lawrence and Arthur Compton were too busy to serve as director
Compton suggested Oppenheimer
Oppenheimer’s mastery of science and engineering concepts impressed Groves
Others opposed this choice
Oppenheimer had not won a Nobel Prize and lacked administrative experience
His wife Kitty and brother Frank had communist sympathies
The Manhattan Project’s primary enrichment plant lay at Oak Ridge, Tennessee
In October 1942, the Army Corps of Engineers purchased 60,000 acres of land
It named the land Clinton Engineer Works in January 1943
Oak Ridge was a city founded to house the tens of thousands of new employees
It was Tennessee’s fifth largest city in 1945
The Oak Ridge plant contained many small facilities
Construction of the world’s second nuclear reactor started on February 2, 1943
The X-10 Graphite Reactor first operated on November 4, 1943
The Y-12 electromagnetic separation plant separated uranium isotopes
This enrichment method based on the cyclotrons was inefficient but low-risk
The K-25 gaseous diffusion plant performed enrichment with gaseous diffusion
It was one of the largest single-roofed buildings in the world
At the time, gaseous diffusion had not been demonstrated to work
It required a barrier that could separate isotopes by their average speeds
The enrichment level of this plant steadily increased as the years went by
The S-1 committee rejected the centrifuge method, so no such plants were constructed
Tests at the X-10 reactor showed that a full-scale reactor was needed to produce
plutonium
Groves hired the DuPont chemical company to construct the plant
DuPont had worked on various war contracts and operated reactors
Since Oak Ridge was close to Knoxville, DuPont decided to construct the plant on the
Columbia River in Washington state
Knoxville was a populated city
Groundbreaking at the Hanford Engineer Works occurred in March 1943
The B-Reactor at Hanford was the world’s first large plutonium generator
Construction started in October 1943
In September 1944, criticality was achieved
Los Alamos
In 1942, scientists worked on the Manhattan Project from across the country
The project’s administration decided to form a centralized laboratory
Oppenheimer wanted the laboratory to be in a remote location
General Groves founded Site Y in northern New
Mexico in 1943
It lay near the Los Alamos Ranch School, 30
miles northwest of Santa Fe
The secret location had a mailing address at a
P.O. box in Santa Fe
Today, Site-Y is known as Los Alamos
National Laboratory
In 1943, Oppenheimer recruited scientists from
across the nation to join Los Alamos
His hires included “Berkeley Luminaries” Hans
Bethe and Edward Teller
Many of the scientists had won Nobel Prizes
Richard Feynman and Emilio Segre
would win Nobel Prizes later
Albert Einstein never joined the Manhattan
Project
He had to create a detonation mechanism that
could rapidly reach supercritical mass
Subcritical masses might produce smaller explosions and blow apart the material
In this case, the bomb pre-detonates, or “fizzles”
Two types of detonation mechanisms were proposed
At first, engineers designed a gun-type plutonium bomb
They dubbed it the “Thin Man” due to its unusual shape
The first shipment of plutonium arrived at Los Alamos in April 1944 from X-10
Emilio Segre realized that reactor-bred plutonium had more impurities than cyclotron-
made plutonium
It contained too much plutonium-240, which tends to start the chain reaction too
early and fizzle out
Mathematician John von Neumann proposed an implosion-type weapon in
September 1943
He relied on earlier work by physicist Seth Neddermeyer
Although more complex, it brought the fuel together more quickly
In 1944, Oppenheimer instructed researchers to abandon the gun method
On August 7th, 1944, General Groves announced that an implosion bomb would be
completed by spring 1945
A uranium gun-type bomb would be finished later in August 1945
The team planned a full-scale test outside Alamogordo, New Mexico
Groves only approved the test after assuring that the nuclear material would be
recovered if the bomb fizzled
Oppenheimer named the test “Trinity” after a
poem by John Donne67
The bomb, nicknamed the “gadget”, used
Hanford B plutonium
A 100-foot-tall tower suspended the bomb to
produce maximum power
Energy from a midair detonation would
expand in a sphere
Observers sat in bunkers 10,000 yards north,
west, and south of the tower
The Trinity test occurred at 5:30 am on July 16th, 1945
The bomb released the same energy as 20,000 tons of TNT
A mushroom cloud rose 7.5 miles into the air
The bomb left a crater 5 feet deep and 30 feet across
The steel tower was completely destroyed68
Nuclear Weapons and International Security Atomic bombing of Japan
Roosevelt unexpectedly died in office on April 12, 1945
Harry Truman replaced him just three months after becoming Vice President
He did not know of the Manhattan Project
General Groves and Secretary of War Henry Stimson discussed the deployment of the
bomb with Truman on April 25
By this time, the Allies had the upper hand in the war against Japan
Nazi Germany surrendered on May 8
The Americans and British planned to invade Japan on November 1 1945
However, the invasion would have cost millions of casualties
On July 26, Allied leaders presented the Potsdam Declaration to Japan
Japan rejected the declaration’s terms of surrender
In July, Leo Szilard and 70 scientists signed a petition against using the bomb
Secretary of State James Byrnes prevented Truman from seeing the petition
Ernest Lawrence wanted the military to publicly demonstrate the bomb
He reasoned that the show of power would compel Japan to surrender
However, a failed test would only encourage the Japanese to keep fighting
Only two bombs had been produced after two years and billions of dollars
It would also remove the element of surprise
Japan might move prisoners of war to bombing targets
The Scientific Advisory Panel rejected the proposal
It concluded that direct military use of the bomb remained the only option
Hiroshima and Nagasaki were selected as targets in summer 1945
Hiroshima was a major port and housed military headquarters
It had not been hit with air raids, so the bomb would have a more striking effect
67
68
“We knew the world would not
be the same. A few people
laughed, a few people cried,
most people were silent.”
– Oppenheimer, on reactions to
the Trinity test
Manufacturing centers Kyoto and Yokohama were also considered
Because Kyoto had historical significance as the former capital, it was rejected69
The seaport and industrial center Nagasaki replaced Kyoto
On August 6th, 1945, the United States dropped an atom bomb on Hiroshima
The bomb nicknamed “Little Boy”70 used a gun-type uranium design
The bomb leveled five square miles of the city and killed 140,000 people
It released the energy of 15,000 tons of TNT
The blast sparked firestorms that burned anything not destroyed by the blast
A radiation flash permanently burned shadows of people and objects onto walls
It etched clothing patterns into skin
The bomb killed or disabled 90% of Hiroshima’s medical personnel
President Truman announced the bombing to the American public over radio
He reasoned that this bomb would “shorten the agony of war”
If Japan did not surrender, he warned, the United States would drop another bomb
The United States accordingly dropped a second bomb on Nagasaki on August 9th
This bomb, named “Fat Man”, was an implosion-type plutonium bomb
It resembled the Trinity Test’s bomb, releasing 21,000 tons of TNT
Nagasaki’s geography limited the damage to 3 square miles, killing 74,000 people
Japan finally surrendered on August 15th
The formal surrender occurred on September 2nd onboard the USS Missouri
American nuclear research after 1945
By 1945, the Manhattan Project rivaled the American automotive industry in scale
It employed 130,000 people and cost $2 billion dollars, or $26 billion in 2015 values
Many employees did not even know they were working on an atomic weapon
The National Laboratories set a standard for federally-funded research
Oak Ridge director Alvin Weinberg termed the federally funded lab system “Big
Science”
Many reporters predicted that atomic power would transform life after the war
New York Times journalist William Lawrence termed the period the atomic age
He had personally witnessed the Trinity Test and the bombing of Nagasaki
Lewis Strauss thought that electricity would become “too cheap to meter”
Newspapers and magazines imagined atomic cars and atomic medicine
The United States did not know if the atomic program should remain controlled by the
military
In October 1945, Congress debated the May-Johnson Bill
According to this proposal, the military would continue managing the program
Fermi and Oppenheimer supported the bill, while Szilard opposed it
In December 1945, the May-Johnson Bill was replaced by the McMahon Bill
This bill gave control of the program to civilians
President Truman signed it into law as the Atomic Energy Act of 1946
The United States Atomic Energy Commission (AEC) took over the nuclear research
program from the army on January 1st, 1947
Five civilians sat on the board of the AEC
It established the National Laboratory system and continued weapons testing
69
70
The Nuclear Regulatory Commission and the Energy Research and Development
Administration replaced the AEC in 1974
In 1977, Jimmy Carter established the US Department of Energy
This agency still manages the United States’ nuclear weapons and energy programs
Nuclear arms race
The United States and Soviet Union became rival superpowers after World War II
American scientists predicted that the Soviet Union would develop an atomic bomb in
the 1950s
The Soviet Union surprised the world by detonating one on August 29, 1949
The superpowers rapidly grew their stockpiles of nuclear weapons
Children learned to perform “duck and cover” drills to prepare for nuclear war71
The next step in atomic escalation involved thermonuclear weapons
Oppenheimer publicly opposed thermonuclear weapons
The United States tested a hydrogen bomb on November 1, 1952 in the Pacific
The Soviets followed suit in August 1953
If either superpower attacked, both sides would be annihilated
This situation has become known as mutually assured destruction (MAD)
Atoms for Peace
The postwar scientific community experienced rifts and regret
The United States found out that Germany had not pursued nuclear weapons72
Many scientists had joined the project for the purpose of pre-empting Germany
Albert Einstein deeply regretted starting the Manhattan Project
In 1947, he told Newsweek that he would not have acted had he known Germany
would not develop the bomb
Oppenheimer told President Truman, “I feel I have blood on my hands”
He pushed for an international nuclear oversight organization
However, neither superpower wanted to give up nuclear weapons73
Supporters of disarmament came under suspicion as communist sympathizers
AEC commissioner Lewis Strauss tried to discredit Oppenheimer
After months of hearings, he had Oppenheimer’s security clearance revoked
Scientists worked to warn against nuclear weapons while also gaining support for atomic
energy
Einstein founded the Emergency Committee of Atomic Scientists (ECAS) in 1946
This group included Leo Szilard and Hans Bethe
They presented and published information promoting peaceful atomic uses
In 1945, Eugene Rabinowitch co-founded the Bulletin of the Atomic Scientists
This non-technical magazine on nuclear weapons exists today as a public reference
on global nuclear issues74
The Bulletin has published the Doomsday Clock since 1947
The Doomsday Clock measures how close we are to atomic apocalypse
71
72
73
74
Progress of the Doomsday Clock
Period 1947 Height of Cold War Thawing of Cold War January 2016
Minutes from midnight 7 2 17 3
Eisenhower moved American policy towards peaceful applications of nuclear energy
From MAD to Atoms for Peace
1953 Eisenhower’s December 8 “Atoms for Peace” speech at United Nations
1954 Atomic Energy Act of 1954 partially repeals 1946 Act; allows civilian nuclear power plants
1957 United Nations creates International Atomic Energy Agency (IAEA) to promote
atomic energy and prevent weaponization
1950s-
60s
Great Britain, France, and China develop nuclear weapons, but have much smaller
stockpiles than the superpowers
1969 Jul 1: United States, Soviet Union, and 60 nations sign Nuclear Non-proliferation Treaty
barring countries from acquiring nuclear weapons
1978 Carter signs Nuclear Non-Proliferation Act preventing the spread of weapons material
but allowing foreign countries to acquire fuel for energy production
All numbers in parentheses refer to the page numbers of the USAD Resource Guide where you
can find the original context of the defined term.
TERMS
Absorption spectrum (13) Set of wavelengths absorbed by an atom
Aether (5) Invisible medium that fills the universe; philosophical substance;
does not exist
Alcohol vapor (40) Substance used in cloud chambers
Alpha particle (31, 35, 38, 43) Positively charged decay particle; equivalent to a helium-4
nucleus; can be blocked by paper; travels at 5% of the speed of
light; blocked by skin; ionizing radiation
Angular momentum (15) Property of the electron which Bohr quantized, modifying the
Rutherford planetary model
Anode (7) Positively charged end of a cathode ray tube; receives an invisible
beam from the anode
Antennae (10) Objects representing atoms; emit thermal radiation according to
classical physics
Antineutrino (37) Antiparticle of the neutrino; released in beta minus decay
Antiparticle (36) Relation between the electron and positron
Aplastic anemia (34) Illness caused by radiation exposure; ended Marie Curie's life
Atomic spectroscopy (13) Use of spectral lines to determine a sample's chemical
composition; used in 1868 to discover helium on the sun
Atomos (5) Greek word for "unable to be cut"
Atoms (5) Tiny units of matter; basic building blocks of the universe
Background radiation (43) Naturally occurring radiation; affects everyone; mostly from radon
Balmer series (16) Set of hydrogen's spectral lines caused by transition to the n=2
energy level
Beta particle (35) Less massive decay particle; can be stopped by aluminum
Big Science (68) Model for federally funded research, as described by Alvin
Weinberg
Bose-Einstein condensate
(25)
New state of matter composed of particles with integer spin;
created in 1995 by Carl Wieman and Eric Cornell via laser cooling
Bosons (25) Particles with integer spin; unaffected by Pauli exclusion principle
Break-even (59) Point at which energy output equals input in fusion reactions
Cathode (7) Negatively charged end of cathode ray tube; emits invisible beam
Cathode ray (7) Beam of electrons produced by cathode ray tube; travels from the
cathode to the anode
Chernobyl accident (54) Worst nuclear power incident in history on April 26, 1986 in the
Soviet Union; released 400 times more radiation than Hiroshima
Cloud (23) Metaphor for arrangement of electrons in the Schrödinger model
Coherent (26) Property of laser light; light waves travelling in phase; creates
good interference patterns
Corpuscule (6) Theoretical infinitely divisible particles proposed by Isaac Newton
Cosmic rays (43) High energy radiation originating from outside the solar system
Critical (49) Situation with constant number of fission events; K = 1
Crystals (34) Subject studied by Pierre Curie before joining his wife's research
Cube (5) Shape associated with earth by Plato
Daughter nucleus (36) Nucleus produced by radioactive decay
Deterministic (22) A Newtonian view of the world
Diamagnetic (24) Materials composed of paired electrons; repelled by magnetic
fields
Directional (26) Property of laser light; light travelling in a uniform direction
DNA (43) Cellular component damaged by ionizing radiation; contributes to
mutations, disorders, and cancer
Electromagnetic spectrum (9) Range of all possible electromagnetic waves
Electron (7, 14, 20) Negatively charged cathode ray particle 1800 times lighter than
hydrogen; atomic component; discovered by J.J. Thomson; resides
at quantized energy levels; releases energy when moving down a
level; used in transmission and scanning electron microscopes
Emission spectrum (13) Set of wavelengths emitted by excited electrons
Endothermic (47) Reaction which consumes energy; Q < 0
Excited state (16) Energy levels above the ground state
Exothermic (47) Reaction which releases energy; Q > 0
Fermion (24) Particles with half-integer spin; includes electrons; two of these
cannot occupy the same quantum position
Ferromagnetic (24) Materials with at least one unpaired electron; includes iron and
nickel; loses magnetic properties above the Curie temperature
Fissile (47) Nuclei that perform fission after colliding with low-energy
neutrons
Fission products (47) Output of a fission reaction
Fissionable (48) Nucleus that only performs fission with fast neutrons
Free radical (43) Neutral atom with unpaired electrons; created by radiation; forms
harmful compounds in the body
Fukushima Daiichi nuclear
accident (54)
Nuclear disaster following an earthquake on March 11th, 2011;
forced evacuations of the surrounding area
Fusion ignition (58) Point at which a fusion reaction becomes self-sustaining
Gamma particle (35, 43) Photon decay particle; high energy; can only be stopped by lead
plating; most destructive to life
Graphite (51, 61) Moderator in first nuclear reactor; made of carbon-12; purchased
in the early days of atomic research
Ground state (15) Lowest allowable energy state of an atom or particle
Heavy water (51) Water with two molecules of deuterium instead of hydrogen; used
as a moderator in Canadian reactors
Ionizing radiation (42) Radiation with enough energy to remove electrons from atoms;
energy > 10 eV; includes X-rays, gamma rays, UV light, alpha
particles, beta particles, and decayed neutrons
Icosahedron (5) Shape associated with water by Plato
Isotopes (30) Atoms with the same number of protons but different numbers of
neutrons; means "the same place" in Greek
Lyman series (16) Set of hydrogen's spectral lines discovered from 1906 to 1914
Magnetic moment (24) Property of the electron; measures tendency to align with a
magnetic field
Magnetic resonance imaging
(34)
Using power magnetics and radio waves to perform diagnostic
imaging of patients
Moderator (50) Component of a nuclear reactor; surrounds the nuclear fuel and
slows down fast neutrons
Monochromatic (26) Property of laser light; light of a uniform frequency
Muon (40) Particle discovered in a cloud chamber
NaI (40, 45) Crystal used in scintillation counters; ingested by patients when
using radioactive tracers
Neutrino (37, 43) Particle released in beta plus decay; first observed in 1950; has no
electric charge and very little mass; does not interact with matter
Neutron (29) Electrically neutral particles in the nucleus; a type of nucleon;
proposed in 1920 by Ernest Rutherford
Non-ionizing radiation (42) Radiation without enough energy to remove electrons from
atoms, e.g. radio waves, microwaves, infrared, and visible light
Nuclear physics (29) Study of the structure and behavior of the atomic nucleus
Nucleon (29) Particle in the nucleus; proton or neutron
Nucleus (7) Dense central core of the atom; contains protons and neutrons;
positively charged
Paramagnetic (24) Materials composed of unpaired electrons; have an overall
magnetic moment
Parent nucleus (36) Nucleus performing radioactive decay
Paschen series (16) Set of hydrogen's spectral lines discovered in 1908
Photon (13) Particle form of light; first proposed by Albert Einstein; massless,
yet still carries momentum
Pitchblende (34) Mineral which contains uranium; studied by Marie Curie
Plasma (58) Collection of superheated atoms represented by a cloud
Positron (36, 40) Antiparticle of the electron; same mass as electron but opposite
charge; very short lifetime outside of a vacuum; discovered in a
cloud chamber
Primordial isotopes (44) Isotopes created with the Earth; includes uranium-238
Probabilistic (22) A quantum view of the world
Probability density (20) Field of probabilities where a particle may reside'
Proton (29) Positively charged particle in the nucleus; a type of nucleon
Psi (20) Greek letter denoting wave functions
Quantum (11) A discrete, fundamental unit of energy
Quantum mechanics (19) Field of physics which provided a unified explanation for quantum
effects; rose in prominence after 1925
Radiation therapy (43) Using targeted ionizing radiation to kill cancerous cells
Radioactive waste (52) Harmful radioactive fission products of uranium-235
Radiometric dating (44) Using the half-life of isotopes in a substance to determine its age;
developed by Willard Libby in the 1940s
Subcritical (49) Situation of decreasing number of fission events over time; K < 1
Sunburn (43) Radiation damage caused by exposure to ultraviolet radiation
from the sun
Supercritical (49) Situation in which the number of fission events increases
exponentially with time; K > 1; used in nuclear weapons
Thermal radiation (10) Radiation emitted by objects above 0 K; generally felt as infrared
radiation
Three Mile Island accident
(53)
Nuclear accident on March 28 1979 in Pennsylvania; worst nuclear
accident in American history but did not have any health impacts
Torbernite (34) Mineral containing uranium; studied by Marie Curie
Tracer (45) Radioactive substance used to track how chemicals participate in
reactions and flow through a system
Uranium hexafluoride (50) Gas used in gas diffusion enrichment
X-rays (34) High energy rays named by Wilhelm Roentgen for their unknown
nature
Units and Constants
Atomic mass number (29) A; total number of neutrons and protons in the nucleus
Atomic number (29) Z; the number of protons in the nucleus; indexes the elements
Becquerel (39) Standard unit of radioactivity since 1975; 1 decay per second
Binding energy (32) Energy required to split a nucleus apart into neutrons and
protons; indicates the stability of an atom; peaks around Z=56
Bohr radius (15) 0.0529 nm; radius of ground state electron orbit in hydrogen atom
Charge of the proton (29) 1.6 × 10−19 coulombs
Critical mass (54) Minimum mass of fissile material for a chain reaction; for
weapons-grade uranium-238, a sphere 6.8 inches in diameter
Curie temperature (24) Upper limit at which ferromagnets have magnetic properties
Curie temperature (39) Standard unit of radioactivity until 1975; 3.7 × 10−10 decays/s
Decay constant (38) λ; corresponds to speed of decay for an isotope
Decay rate (39) Also known as radioactivity; decays per second
Electron volt (15) 1.6 * 10^-19 J; energy of an electron accelerated by a 1 volt
potential difference
Energy level (14) A specific, quantized, stable orbit of the electron
Femtometer (30) 10−15 meters; the approximate radius of a nucleus
Fermi (30) See femtometer
Frequency (9) Speed of oscillation of a wave; measured in hertz
Half-life (39) Time for half of a sample of an isotope to decay; quantifies atomic
stability
Hertz (9) Measures frequency of waves; equal to 1 oscillation per second
Ionization energy (16) Energy required to completely remove an electron from an atom;
for hydrogen, 13.6 eV
Magic numbers (33) Recurring numbers of neutrons and protons which contribute to
stability; 2, 8, 20, 28, 50, 82, 126
Momentum (13) Property of objects with mass and photons
Multiplication factor K (49) Average number of neutrons released in a fission event that will
trigger another fission event; controls criticality
Nanosecond (12) Delay before electron ejection in the photoelectric effect
Neutron number (29) N; the number of neutrons in the nucleus
Orbital magnetic quantum
number (24)
𝑚𝑙; can be integer values from -l to +l; associated with the
Zeeman effect
Orbital quantum number
(24)
𝑙 ; can be non-negative integer values
Planck's constant (11) 6.63 × 10−34 Joule seconds; central in quantum mechanics
Principal quantum number
(24)
See quantum number
Q value (46) The energy released by one nuclear reaction event; the difference
in mass between products and reactants
Quantum number (15, 23) Index of electron energy; only positive integers; represented by n
Relative atomic mass (29) Mass number listed on periodic tables; average mass of all
isotopes of an element weighted by abundance
Rem (42) Measure of dosage commonly used in the United States; equals
1/100 sievert
Rydberg constant (14) 1.097 × 107𝑚−1
Second (27) Unit defined in 1967 as the time of 9,192,631,770 oscillations of
cesium-133 through its energy states; most accurate SI unit
Sievert (42) Measures dosage of ionizing radiation; represents the effect of 1
joule of radiation on 1 kg of absorbing material
Spin quantum number (24) 𝑚𝑠; for electrons, can be +1/2 or -1/2
Temperature (27) Measures a substance's kinetic energy
Threshold energy (47) Minimum kinetic energy required for an endothermic reaction
Unified mass unit (29) u; 1/12 the mass of a carbon-12 atom; the mass of one proton or
one neutron; 1.66 ∗ 10−27 kg
Wavelength (9) Distance between successive peaks in a wave
Equations
Atomic mass number (29) A; total number of neutrons and protons in the nucleus
Alpha decay reaction (36) 𝑋𝑍𝐴 → 𝑌𝑍−2
𝑍−4 + 𝐻𝑒24
Beta negative decay reaction
(36)
𝑋𝑍𝐴 → 𝑌𝑍+1
𝐴 + 𝑒−
Beta plus decay reaction (36) 𝑋𝑍𝐴 → 𝑌𝑍−1
𝐴 + 𝑒+
de Broglie hypothesis (17) 𝜆 =ℎ
𝑝
Decay rate equation (39) 𝑅 = 𝑅0𝑒−𝜆𝑡
Differential wave equation
(19)
Classical equation; describes behavior of macroscopic waves
Einstein's relation (29, 32) 𝐸 = 𝑚𝑐2; explains mass difference between nucleon and nuclear
weights
Energy levels in hydrogen
(15) 𝐸𝑛 = 13.6
𝑒𝑉
𝑛2
Exponential decay (38) 𝑁 = 𝑁0𝑒−𝜆𝑡
Gamma decay reaction (37) 𝑋∗ → 𝑋 + 𝛾
Half life equation (39) 𝑡ℎ =ln 2
𝜆
Heisenberg uncertainty
principle (23)
Δ𝑥Δ𝑝 ≥ℎ
2𝜋; stipulates that momentum and position of a particle
cannot both be known
Lawson’s criterion (58) nτ > some number for plasma to occur; n = plasma ion density; t
= plasma confinement time
Newton's laws of motion (19) Classical laws; describe the behavior of macroscopic particles
Nuclear notation (29) 𝑋𝑍𝐴 ; A = mass number; Z = atomic number
Planck's relationship (11) 𝐸 = 𝑛ℎ𝑓; relationship between energy of an oscillating particle
and its frequency
Radii of electrons in
hydrogen (15)
𝑟𝑏 = 𝑛2𝑎0
Radius of the nucleus (30) 𝑟 = 𝑟0𝐴13
Schrödinger equation (19) 1925 description of matter waves’ behavior; cannot be derived
from fundamental equations: purely based on experimental results
The Rydberg formula (14) 1
𝜆= 𝑅𝐻 (
1
𝑚2 −1
𝑛2); describes the wavelengths of spectral lines in
hydrogen
Wave functions (20, 23) Solutions to the Schrödinger equation; labeled by the Greek letter
psi; describes electrons in the Schrödinger model
Elements and Isotopes
Actinium (39) Element which can enter a decay chain
Aluminum (27) Element used in atomic clocks
Americium-231 (44) Isotope in smoke detectors; alpha-decays into neptunium-1237
Argon (44) Element used in radiometric dating
Barium (48) Half as massive as uranium; bombarded by Otto Hahn and Fritz
Strassman; can be produced in fission of uranium-235
Beryllium (31) Discovered ca. 1930; emits radiation if struck with alpha particles
Bismuth-212 (39) Isotope produced in decay chain of thorium
Boron (51) Neutron-absorbing material used in control rods
Californium (31) All isotopes heavier than this element do not occur naturally
Carbon-12 (29, 51) Isotope used to define the unified mass unit; found in graphite
Carbon-14 (36, 44) Isotope which decays into nitrogen-14 through beta decay;
measured in radiometric dating
Cesium-133 (27) Isotope used in atomic clocks; defines the second in the SI system
Cobalt-60 (43) Isotope used in food irradiation
Deuterium (31, 50, 58) Isotope of hydrogen with a proton and neutron; useful moderator;
used in fusion; found in seawater
Fluorine (50) Element combined with uranium in gas diffusion enrichment
Gallium (7) Element predicted by Mendeleev's periodic table before its
discovery; "doubly magic"; has high atomic stability
Helium-4 (13,24, 25, 32, 55) Isotope discovered using atomic spectroscopy in 1868; found on
the sun; a noble gas; used in lasers; produced in nuclear fusion
Hydrogen (6, 14, 27, 34, 40,
58)
Element discovered by Antoine Lavoisier and modeled by the
Rydberg formula; used in atomic clocks and bubble chambers;
aligned by magnetic waves in magnetic resonance imaging;
undergoes fusion; lightest and most abundant element
Iodine-131 (45) Radioactive isotope used in radioactive tracing; synthetic
Iron (24, 32) Ferromagnetic material; very stable element
Krypton (48) Element produced in the fission of uranium-235
Lead (35) Element used to shield against gamma radiation
Lithium (24) An alkali metal
Lithium-7 (46) Isotope used by Ernest Walton and John Cockcroft in the first
nuclear reaction
Mercury (17, 27) Element used in James Franck and Gustav Hertz's experiment with
a vacuum tube; used in atomic clocks
Neon (24, 25) Noble gas used in lasers
Neptunium (39, 48) Artificial element; can enter a decay chain; discovered by Enrico
Fermi by bombarding uranium
Nickel (18, 24, 32) Element used in the Davisson-Germer experiment which proved
wave-particle duality; ferromagnetic material; very stable element
Nitrogen-14 (30, 56) Gas used by Ernest Rutherford in observing the emission of
hydrogen nuclei after nuclear collisions; produced in the beta
decay of carbon-14; present in the CNO cycle
Oxygen (6, 32, 56) Element initially discovered by Antoine Lavoisier; "doubly magic";
has high atomic stability; present in the CNO cycle
Phosphorous (37) Element studied by Irene Joliot-Curie and her husband Frederic
Plutonium-239 (48, 52, 64) Discovered by Enrico Fermi by bombarding uranium; carcinogenic;
used in nuclear weapons; produced in breeder reactors; desired
product of the Hanford Engineer Works; cannot be used in gun-
type weapons; powered Fat Man bomb
Polonium (34) Element discovered by Marie Curie and Pierre Curie
Potassium-40 (42) Isotope which provides an annual dose of 0.4 mSv if ingested
Radon-222 (43) Isotope responsive for most background radiation; causes lung
cancer; found as a dense inert gas
Rubidium (27) Gas cooled to 50 trillionth K by Stanford researchers in 2015
Sodium (24, 51) Alkali metal whose emission spectrum has split lines; used in
liquid form as reactor coolant
Strontium (27, 48) Element used in atomic clocks; produced in uranium-235 fission
Tellurium (36) Lightest known element to perform alpha decay
Thorium (39) Element which can enter a decay chain
Thorium-234 (36) Isotope produced by the alpha decay of uranium-238
Tritium (31) Radioactive isotope of hydrogen with two neutrons and a proton
Uranium (48) Heaviest known element in the 1930s
Uranium-235 (48, 67) Isotope that produces a usable chain reaction; releases three
neutrons during each fission; powered the Little Boy bomb
Uranium-238 (34, 40, 49) Radioactive isotope studied by Marie Curie; alpha-decays into
thorium-234 decay chain and replenishes the natural abundance
of radium-226; absorbs neutrons without performing fission
Xenon (48) Element produced in the fission of uranium-235
Theories and Phenomena
Alpha decay (36) Decay involving the emission of a helium nucleus
Atomic theory (5) Theory that all matter is composed of indivisible atoms
Beta decay (36) Decay involving the emission of an electron or positron
Beta minus decay (36) Decay involving the emission of an electron
Beta plus decay (36) Decay involving the emission of a positron
Chain reaction (48) Neutrons from one fission event triggering more events
CNO cycle (56) Reactions in very hot, large stars; converts hydrogen to helium via
carbon, nitrogen, and oxygen; proposed by Hans Bethe in 1939
Compton scattering (13) Discovered in 1923; scattering of X-ray radiation off free electrons;
unexplainable by the wave model of light and classical physics
Corpuscular theory (6) Theory that all matter contains infinitely divisible corpuscules
Corpuscular theory of light
(7, 9)
Isaac Newton’s theory in Opticks (1704) that light consists of
weightless balls; explains reflection but not refraction or
diffraction
Correspondence principle
(16)
Proposed by Niels Bohr; states that quantum theory should align
with classical expectations at large scales
Coulomb barrier (55) Energy barrier preventing fusion reactants from colliding
Dalton's atomic theory (6) Principles in John Dalton’s 1808 A New System of Chemical
Philosophy stating that identical atoms comprise an element;
atoms cannot be created, destroyed, or divided, and (re)combine
in simple ratios in chemical reactions
de Broglie hypothesis (17) Relation of a particle's momentum with its wavelength
Decay (39) Transformation of parent isotopes to daughter isotopes through
the emission of alpha, beta, or gamma particles
Decay chain (39) Radioactive daughter nucleus performing more decay; occurs with
thorium, uranium, actinium, and neptunium
Doppler cooling (27) Method of selectively slowing atoms in laser cooling
Doppler effect (27) Frequency shift caused by relative motion between the observer
and wave emitter; used in laser cooling
Double slit interference (9) Discovered by Thomas Young in 1803; constructive and
destructive interference formed when light enters two narrow slits
Electron capture (37) Absorption of an orbiting electron by a nucleus; emits a neutrino
Enrichment (49) Increasing proportion of uranium-235 in mined uranium
Fizzle (65) Situation in which a nuclear weapon prematurely detonates
without reaching its expected yield
Gamma decay (37) Process in which a nucleus transitions from a high energy to a low
energy state and releases a gamma ray photon
Heisenberg uncertainty
principle (23)
Axiom that the position and momentum of a particle cannot both
be known with absolute precision
Induced radioactivity (37) Artificial creation of an unstable isotope artificially
Inertial confinement fusion
(59)
Using high-power lasers to heat and compress a pellet of
deuterium and tritium to start fusion; utilized by the NIF
K-capture (37) Form of electron capture that absorbs it from the "K" shell
Laser cooling (27) Using lasers to slow atoms; draws on photon momentum
Law of conservation of
matter (6)
Observation that mass is conserved in chemical reactants; noted
by Antoine Lavoisier in the late eighteenth century
Maxwell's theory of
electromagnetism (9)
Description of light as a wave made up of oscillating electric and
magnetic fields
Meltdown (41) Result when the core of a nuclear reactor overheats and melts
Mutually Assured
Destruction (69)
Scenario in which states completely destroy each other in mutual
nuclear weapon attacks
Nuclear fission (47) Heavy nucleus splitting into two lighter nuclei and releasing
energy; triggered by collisions
Nuclear fusion (55) Two small nuclei colliding to form a larger nucleus
Nuclear reaction (46) Two nuclei colliding to form different nuclei; analogous to
chemical reactions
Pauli exclusion principle (24) Axiom that no two electrons have the same set of quantum
numbers, except for bosons
Photoelectric effect (12) First observed by Heinrich Hertz in 1887; release of electrons by
metals illuminated with ultraviolet light
Planetary model (7) Model of the atom inspired by Rutherford’s discovery of the
nucleus; electrons orbiting a dense positively charged nucleus
Plum pudding model (7) Model of the atom proposed by J.J. Thomson; featured a sea of
electrons suspended in a positively charged sphere
Population inversion (25) Creation of sample with more excited atoms than in the ground
state
Proton-proton chain (56) Multi-step solar fusion reaction; converts four protons into
helium-4, positrons, neutrinos, and gamma rays; proposed by
Hans Bethe in 1939
Quantum theory (9) Theory that energy and matter is quantized
Quantum tunneling (20, 55) Implication of the Schrödinger equation that low energy particles
can overcome tall potential barriers; basis for scanning tunneling
microscope; lets particles in nuclear fusion cross Coulomb barrier
Radioactive decay (35) Spontaneous emission of radiation associated with a
transformation from an unstable nucleus to a stable nucleus
Radioactivity (34) Spontaneous radiation emission; studied by Curies and Becquerel
Refraction (9) Light bending around narrow apertures or corners
Schrödinger model (23) Model of the atom which describes electrons with wave functions;
features a "cloud" of electrons; the modern model of the atom
Solar wind (56) Collection of low mass particles ejected by the Sun
Spontaneous emission (25) An atom releasing a photon in a random direction
Stimulated emission (25) Causing atom to transition to a lower energy level and release a
photon; used in lasers
Strong nuclear force (32) Attractive force between nucleons; counteracts repulsive force
between protons
Thermonuclear fusion (55) Fusion of nuclei at extremely high temperatures
Ultraviolet catastrophe (11) Finding that blackbody radiation emits little ultraviolet light
Wave-particle duality (18) Notion that light and matter exhibit properties of both waves and
particles; seen in double slit experiment
Zeeman effect (24) Fine splitting of spectral lines when substance is placed in a
magnetic field
Devices
Atomic clock (27) Timekeeping device; relies on precise frequencies of atomic
transitions
B Reactor (64) First plutonium-generating reactor; located at Hanford Engineer
Works
Blackbody (10) Idealized object that releases all radiation it absorbs to remain in
thermal equilibrium
Boiling water reactor (52) Reactor using water as moderator, coolant, and source of steam
Breeder reactor (52) Reactor producing useful fissile material, plutonium-239
Bubble chamber (40) Traces the path of ionizing radiation; uses liquid hydrogen;
invented by Donald Glaser in 1952
Cathode ray tube (7) Device consisting of glass tubes with vacuums; creates a cathode
ray; used in CRT televisions and computer monitors; used in many
experiments in the 1800s
Cloud chamber (40) Traces path of ionizing radiation; uses saturated vapor and piston
Control rod (51) Component of a nuclear reactor; absorbs neutrons and regulates
the speed of the chain reaction
Cyclotron (62) First particle accelerator; invented by Ernest O. Lawrence
Doomsday Clock (69) Concept created by the Bulletin of the Atomic Scientists; measures
how close the world is to nuclear Armageddon
EBR-1 Reactor (52) First reactor to generate electricity in 1951; located in Idaho,
Fat Man (67) Plutonium implosion nuclear weapon; dropped on Nagasaki
Gas centrifuge (50) Uses rapidly rotating cylinder to separate uranium-235 from
uranium-238
Gas diffusion enrichment
(50)
Uses semi-permeable membranes to separate uranium-235 from
uranium-238
Geiger counter (40) Radiation detector; uses tube of inert gas; creates clicking sound
Generation IV reactor (53) Next generation nuclear reactor design; minimizes waste,
enhances safety, and prevents nuclear proliferation
Gold foil apparatus (7, 30) Device which Ernest Rutherford, Hans Geiger, and Ernest Marsden
used to discover the nucleus; contained a beam of positive alpha
particles which deflected off a gold foil
Gun-type (54) Detonation mechanism where two pieces of fuel are shot together
HeNe laser (26) Common laser used in laboratories and classrooms
Implosion-type (54) Detonation mechanism in which explosives compress a subcritical
fuel mass; used in modern nuclear weapons
ITER (59) World's largest experimental fusion reactor; funded by 7 countries
Joint European Torus (59) Tokamak fusion reactor located in the UK
K-25 (63) Gaseous diffusion plant at Oak Ridge; one of the largest single-
roofed buildings in the world
Large Hadron Collider at
CERN (46)
Advanced particle accelerator capable of accelerating particles to
energies greater than 1 TeV
Laser (26) Device using stimulated emission to create a beam of
monochromatic, directional, coherent light
Laser enrichment (50) Uses tuned lasers to separate uranium-235 from uranium-238;
requires little energy
Little Boy (67) Uranium gun-type nuclear weapon; dropped on Hiroshima
Magnetic separation
enrichment (50)
Uses a magnetic field to separate uranium-235 and uranium-238
National Ignition Facility (59) Largest ICF device in the world; at Lawrence Livermore National
Labs in California; uses lasers to compress a hydrogen pellet
Nuclear reactor (50) Device which initiates and controls a nuclear chain reaction;
harnesses reaction energy for power generation
Particle in a box (20) Physics model which describes an energized particle trapped in a
1 dimensional space bounded by infinitely high potential walls
Photomultiplier tube (40) Component of a scintillation counter
Pile-1 (63) Enrico Fermi's first nuclear reactor; built at the University of
Chicago
Pressurized water reactor
(52)
Reactor which uses a separate cooling loop of water to produce
steam; common in the United States; prevents fuel leakage
Proportional counters (40) Sophisticated form of Geiger counters; measures energy of
radiation
Scanning tunneling
microscope (20)
Uses quantum tunneling to achieve resolutions of 0.1 nm using
electrons
Schrödinger's cat (22) Scenario involving a simultaneously dead and alive cat;
demonstrates the multiple states of a quantum system
Scintillation counter (40) Radiation detector; relies on NaI crystal and a photomultiplier
tube; can determine the energy of emitted radiation
Smoke detector (44) Device using a stream of alpha-particles produced by americium-
241
Thermonuclear weapon (57) Nuclear weapon which uses a fission bomb to trigger a
thermonuclear explosion
Thin Man (65) Gun-type plutonium fission bomb; abandoned due to poor quality
of available plutonium
Tokamak (58) Toroidal shaped device that confines a plasma using magnetic
fields; developed in the Soviet Union during World War II
Tokamak Fusion Test Reactor
(TFTR) (59)
Tokamak fusion reactor at Princeton; never reached break-even
Transmission electron
microscope (18)
Device which relies on the wave properties of electrons to achieve
very fine image resolutions; accelerates electrons to 100 keV; has a
resolution on the order of 0.0037 nm
Trinity Bomb (65) First nuclear weapon ever detonated; implosion-type
Tsar Bomba (57) Most powerful nuclear weapon detonated; a hydrogen bomb; as
powerful as 50 million tons of TNT
U.S.S. Missouri (67) Ship which hosted the former surrender of Japan
X-10 (63) Graphite reactor at Oak Ridge
Y-12 (63) Electromagnetic separation plant at Oak Ridge; second manmade
nuclear reactor
Awards and Publications
1901 Nobel Prize in Physics
(34)
First Nobel Prize in Physics; awarded to Wilhelm Roentgen for
discovering X-rays
1903 Nobel Prize in Physics
(34)
Awarded to Marie Curie, Pierre Curie, and Henri Becquerel for
their discoveries involving radioactivity
1911 Nobel Prize in
Chemistry (34)
Awarded to Marie Curie, Pierre Curie, and Henri Becquerel for
their discoveries involving radioactivity
1921 Nobel Prize (13) Awarded to Albert Einstein for explaining the photoelectric effect
using photons
1925 Nobel Prize in Physics
(17)
Awarded to James Franck and Heinrich Hertz for demonstrating
that an atom's absorption energies match its emission energies
1935 Nobel Prize in
Chemistry (38)
Awarded to the Joliot-Curies for discovering induced radioactivity
1960 Nobel Prize in
Chemistry (44)
Awarded to Willard Libby for developing carbon dating
1967 Nobel Prize (57) Awarded to Hans Bethe for explaining stellar energy production
1997 Nobel Prize in Physics
(27)
Awarded to three physicists for developing laser cooling
A New System of Chemical
Philosophy (6)
Published in 1808 by John Dalton; included Dalton's basic atomic
principles
Atomic Energy Act of 1946
(68)
Placed atomic research under civilian control; passed by Harry
Truman
Atomic Energy Act of 1954
(69)
Signed by Eisenhower; permitted the development of civilian
nuclear power plants
Atoms for Peace (69) Address delivered by President Eisenhower to the United Nations;
outlined a commitment to peaceful atomic uses
Bulletin of the Atomic
Scientist (68)
Non-technical magazine on nuclear weapons and nuclear security
founded by Eugene Rabinowich; source of the Doomsday Clock
May-Johnson Bill (68) Bill proposed in October 1945; would continue military oversight
over atomic research; opposed by Szilard
McMahon Bill (68) Bill proposed in December 1945 to oppose the May-Johnson Bill;
placed atomic research under civilian control; incorporated in the
Atomic Energy Act of 1946
Mr. Tompkins in Wonderland
(23)
Written in 1940 by George Gamow; describes a bank teller
exploring a quantum jungle with strange animals
New York Times (68) Newspaper of William Lawrence
Newsweek (69) Quoted Einstein's opposition to the Manhattan Project
Nuclear Non-Proliferation
Act of 1978 (69)
Signed by President Carter; prevented the spread of nuclear
materials for weapons use, but allowed for peaceful use
Nuclear Non-Proliferation
Treaty (69)
Signed in 1968 by 69 nations; prevented new nations from
acquiring nuclear weapons
Opticks (6, 9) Published in 1704 by Isaac Newton; suggested the corpuscular
theory of light
Periodic Table of Elements
(6)
Organization system for elements created by Dmitry Mendeleev;
organized elements by atomic weight
Potsdam Declaration (66) Allied leaders present terms of surrender to Japan
Numbers
-1/2 (24) Possible spin quantum number value for electrons
0 (10, 20, 25) Minimum temperature in Kelvin for a body to release thermal
radiation; absolute 0 in Kelvin; classical probability that a particle
will cross a high potential wall; temperature of the Bose Einstein
condensate
6.63 × 10−34 (11) Value of Planck's constant in Joule-seconds
10−33 (42) Energy above which radiation is considered ionizing, in eV
9.1 × 10−31 (30) Mass of one electron, in kilograms
1.66 × 10−27 (29) Mass of one unified mass unit, in kilograms; mass of a proton or
neutron, in kilograms
10−19 (13) Approximate energy of a photon in Joules
1.6 × 10−19 (15, 29) Energy of an electron accelerated across a 1-volt potential
difference in Joules; charge of a proton in Coulombs
10−15 (30) Approximate nuclear radius in meters; 1 femtometer, in meters
1/50 trillion (27) Temperature in Kelvin to which Stanford researchers were able to
supercool rubidium in 2015
10−14 (30) Rutherford's estimate of the nuclear radius, in meters
1 trillionth (44) Portion of carbon that is carbon-14
10−10 (30, 35) Radius of an atom's electron cloud in meters; lifespan of a
positron in seconds
10−9 (59) Time it takes for the NIF to achieve ignition, in seconds
1.097 × 107 (14) Value of the Rydberg constant in m^-1
1/70 thousand (27) Average velocity of molecules in the supercooled rubidium
produced by Stanford researchers, in mm/s
5.486 × 10−4 (30) Mass of one electron, in unified mass units
0.0037 (18) de Broglie wavelength of electrons in a transmission electron
microscope in keV
0.02 millisieverts (42) Dosage of a chest X-ray
0.0529 nanometers (15) Value of the Bohr radius
0.1 (22, 53) Resolution of a scanning tunneling microscope; annual dosage to
a person living 50 miles from a nuclear power plant, in
microsieverts
1/3 (53) Fraction of the world's nuclear energy produced by the United
States
0.4 (42) Dosage of potassium-40 if ingested in millisieverts
0.4 - 0.7 (22) Distance from the sample in a scanning tunneling microscope in
nanometers
1/2 (24) Possible spin quantum number value for electrons
0.511 (30) Mass of one electron in mega-electron volts
0.7 (49) Percent abundance of uranium-235 in nature
1 (12, 42, 44, 46) Number of nanoseconds delay before electron ejection in the
photoelectric effect; dosage which causes radiation sickness, in
sieverts; quantity of americium-241 in a smoke detector, in
micrograms; scale of the energy released by one nuclear reaction,
in MeV
2 (16, 33, 34, 35, 59, 67, 69) Associated with the Balmer series; a magic number; Nobel Prizes
awarded to Marie Curie; Denver receives this times more radiation
annually than the national average; size of the pellet employed by
the NIF, in mm; billions spent by the Manhattan Project; least
minutes the Doomsday Clock has been from midnight
2 - 3 (14) Transition of the hydrogen electron which produces red light
2.5 (48) Average number of neutrons released by fission of uranium-235
3 (48, 69) Maximum number of neutrons released by fission of uranium-235;
current setting of the Doomsday Clock in minutes from midnight
3 - 4 (49) Percent abundance of uranium-235 in nuclear fuel
4 (5, 42) Basic elements as envisioned by Plato; minimum
4.9 (17) Energy lost by an electron colliding with mercury in eV
5 (6, 35, 42, 66) Fatal radiation dosage in sieverts; principles in Dalton's atomic
theory; percent of the speed of light which an alpha particle
travels at; depth in feet of the Trinity test crater
6.2 (42) Average background annual dosage in the United States, in
millisieverts
6.8 (54) Size of a critical mass sphere of weapons grade uranium, in cm
7 (59, 69) Members of ITER; minutes to midnight at Doomsday Clock’s
creation
7.5 (66) Height in miles of the Trinity mushroom cloud
7.6 (49) Average binding energy per nucleon in uranium-235, in
MeV/nucleon
8 (33, 42) Magic number; lethal dosage of radiation, in sieverts
8.5 (49) Average binding energy per nucleon in medium-sized fission
products, in MeV/nucleon
9 (41) Magnitude of the earthquake which triggered the Fukushima
Daiichi nuclear accident
10 (58, 62) Half-life of tritium, in years; original estimate of uranium-235
critical mass
10.4 (57) Energy release of the first hydrogen bomb, in megatons TNT
10.9% (52) World's energy production generated by nuclear reactors
13.6 (16) Ionization energy of hydrogen in eV
15 (7, 62) Diameter of shell mentioned by Rutherford when he commented
on the results of the gold foil experiment; time it took for
President Roosevelt to approve the NDRC, in minutes
19.5% (52) United States' energy production generated by nuclear reactors
20 (33) Mass number below which stable atoms contain equal numbers of
neutrons and protons; a magic number
23.5 (52) Half-life of uranium-239, in minutes
24.68 (56) Energy released in the proton-proton chain, in MeV
25 (56) Abundance of helium in the Sun by mass percent
26 (67) Total budget of the Manhattan project, in billions of 2015 dollars
28 (33) A magic number
30 (13, 52, 58, 66) Countries operating nuclear reactors as of 2015; liters of seawater
required to collect 1g of deuterium; width in feet of the Trinity test
crater
50 (22, 33, 57) Probability that Schrödinger's cat is dead or alive; a magic
number; energy release of Tsar Bomba, in millions of tons of TNT
56 (32) Mass number with maximum atomic stability
60 (32) Mass number above which binding force decreases
62 (69) Countries which signed the Nuclear Non-Proliferation Treaty
64 (6) Elements known to Dmitri Mendeleev
70 (66) Scientists who signed Leo Szilard's petition to demonstrate the
bomb to the Japanese
74 (56) Abundance of hydrogen in the Sun by mass percent
75% (52) France's energy production generated by nuclear reactors
82 (33) A magic number
83 (33) Mass number above which no stable isotopes exist
85 (62) Amount of money obtained by Vannevar Bush for the purpose of
constructing uranium enrichment plants, in millions of dollars
90 (7, 49) Degrees some particles were deflected in the gold foil experiment;
percent abundance of uranium-235 in nuclear weapons
92 (29, 48) Protons in uranium-238; atomic number of uranium
93 (48) Atomic number of neptunium
94 (48) Atomic number of plutonium
98 (31) Mass number of californium
99.99% (31) Proportion of hydrogen-1 in all isotopes of hydrogen
100 (18, 42, 48, 64) Rems in a sievert; dose above which cancer risks increase, in
millisieverts; energy of a fission reaction, in MeV; height of the
steel tower used in the Trinity test, in feet; energy of electrons in a
transmission electron microscope, in keV
126 (33) A magic number
146 (29) Number of neutrons in uranium-238
300 (27) Years it takes for the first cesium atomic clock to lose one second
400 (54) The Chernobyl accident released this times more radiation than
the Hiroshima bomb
400-700 (18) Wavelength of visible light, in nanometers
438 (52) Number of operational power generation reactors as of 2015
450 (57) Order of magnitude with which first hydrogen bomb was more
powerful than the Nagasaki bomb
500 (27, 59, 62) Average velocity of molecules in room temperature gas in m/s;
power output of the NIF, in trillions of watts; millions of dollars
allocated to the Manhattan Project in 1942
632.8 (27) Wavelength of HeNe laser light, in nanometers
653 (56) Tons of helium produced by the Sun every second
656.3 (14) Wavelength of the red line in the hydrogen spectrum in
nanometers
657 (56) Tons of hydrogen processed by the sun every second
931.49 (29) Mass of one unified mass unit, in MeV/c2
938.28 (30) Mass of one proton in MeV
939.57 (30) Mass of one neutron in MeV
1,000 (10, 59) Kelvin at which objects release radiation in the infrared band;
when firing a laser pulse, the NIF consumes this much times more
power than the entire United States
1,800 (7) Order of magnitude with which hydrogen atom is more massive
than a cathode ray particle
1,200 (62) Tons of imported uranium stored at Staten Island in the
Manhattan Project`
1,600 (40) Half-life of radium-226, in years
21,000 (67) Energy release of Fat Man, in tons of TNT
2,403 (62) Deaths at Pearl Harbor
3,000 (38) Artificial radioactive isotopes created in reactors and particle
accelerators
5,730 (44) Half-life of carbon-14, in years
6,000 (61) Initial value of uranium oxide and graphite suggested by the
Advisory Committee on Uranium, in dollars
10,000 (58) Energy of 1 gram of deuterium, in liters of gasoline
15,000 (67) Energy release of Little Boy, in tons TNT
20,000 (50, 66) Tons of TNT with energy equivalent to 1 ton of uranium or the
Trinity bomb
24,000 (52) Half-life of plutonium-239, in years
4.4 × 104 (49) Energy density of gasoline, in J / g
50,000 (44) Maximum age of an item for carbon dating, in years
74,000 (67) Immediate deaths resulting from the Fat Man bombing
100,000 (30, 61) Order of magnitude that the atom is larger than the nucleus;
initial value of uranium oxide and graphite suggested by the
Advisory Committee on Uranium, in 2015 dollars
130,000 (67) Employees of the Manhattan Project at the end of the war
140,000 (67) Immediate deaths resulting from the Little Boy bombing
500,000 (54) Maximum energy of a fission bomb, in tons TNT
107 (55) Temperature at which nuclear fusion occurs, in Kelvin
5 × 107 (44) Minimum half-life of a primordial isotope for it to be detectable
108 (59) Temperature reached by the deuterium pellet in the NIF, in Kelvin
200 million (59) Maximum temperature reached by the TFTR, in Kelvin
300 million (27) Years taken for modern cesium atomic clocks to lose one second
4.5 × 109 (44) Half-life of uranium-238, in years; age of the Earth, in years
4.6 billion (40) Age of the Solar System, in years
9,192,631,770 (27) Oscillations of cesium-137 per second
3.7 × 1010 (39) 1 Curie in decays per second
8.2 × 1010 (49) Energy density of uranium-235, in J/g
1011 (43) Flux of neutrinos on Earth's surface, neutrinos per sq cm/s
1014 s/cm3 (58) Minimum value of Lawson's criterion for deuterium-tritium fusion
1016 s/cm3 (58) Minimum value of Lawson's criterion for deuterium-deuterium
fusion
Places
Alamogordo (65) New Mexico location of the Trinity test
Ancient Greece (5) One of the first cultures to theorize atoms; home to Democritus,
Leucippus, Plato, Aristotle
Arco, Idaho (52) Site of the first nuclear reactor which generated electricity
Australia (57) Home of Mark Oliphant
Austria (19) Home of Erwin Schrödinger
California (59) Location of Lawrence Livermore National Laboratory
Canada (51, 62) Country which uses many heavy-water reactors; provided uranium
for the Manhattan Project
CERN (46) Location of the Large Hadron Collider
China (59) ITER member state
Colorado (62) Site of American uranium mines for the Manhattan project
Denmark (14) Home of Niels Bohr
Denver, Colorado (43) City in the United States with high cosmic radiation exposure due
to its high altitude
England (6, 31, 46, 48, 56, 59,
62)
Home of John Dalton, James Chadwick, John Cockcroft, Arthur
Eddington; site of the Joint European Torus; estimated the critical
mass of uranium-235 to be 10 kg
France (6, 17, 34, 52, 59) Home of Antoine Lavoisier, Joseph Proust, Louis de Broglie, Marie
Curie, Pierre Curie, Henri Becquerel; generates 75% of its energy
with nuclear power; site of ITER
Fukushima Daiichi (41) Experienced a major nuclear accident in 2011
Germany (11, 34, 48, 61) Home of Albert Einstein, Max Planck, Wilhelm Roentgen, Otto
Hahn, Fritz Strassman; home of the Nazi Party; led by Adolf Hitler
Hiroshima (67) Japanese city targeted by Little Boy
Hungary (48) Home of Leo Szilard
India (5, 59) Early culture that theorized atoms; home to Kanada; ITER member
Ireland (46) Home of Ernest Walton
Italy (61) Country with a fascist government; ruled by Benito Mussolini
Japan (41) Location of Fukushima Daiichi nuclear power plant
Japan (59) ITER member state
Knoxville (64) Populated city located close to the Oak Ridge site
Kokura (67) Japanese manufacturing center; considered for nuclear bombing
Korea (59) ITER member state
Kyoto (67) Former capital of Japan and center of industry; considered for
targeting but rejected due to its historical significance
Nagasaki (67) Japanese seaport and center of industry; targeted instead of
Kyoto by the Fat Man bomb
Netherlands (9) Home of Christiaan Huygens
Oak Ridge (63) City founded to house workers at the Clinton Engineer Works
Pearl Harbor (62) American naval base attacked by Japan on December 7, 1941
Pennsylvania (52) Site of the Three Mile Island accident
Poland (34, 61) Homeland of Marie Curie; invaded by Germany in September
1939
Racquet court (51) Location on the University of Chicago campus where the first
nuclear reactor was constructed
Rural eastern Tennessee (63) Site picked for the Oak Ridge nuclear plants
Russia (59) ITER member state
Santa Fe (64) Location of the P.O. Box of Los Alamos
Scotland (9) Home of James Clerk Maxwell
Soviet Union (52) First country to connect a nuclear reactor to the power grid
Staten Island (62) Storage site for imported uranium during the Manhattan project
Switzerland (14) Home of Johann Balmer
United States (13, 40, 52, 59) Home of Arthur Compton, Donald Glaser, Willard Libby; generates
19.5% of its energy with nuclear power; world's largest producer
of nuclear power; ITER member state
Washington (64) State occupied by the Hanford Engineer Works
Yokohama (67) Japanese manufacturing center; possible target for nuclear bomb
Organizations
Advisory Committee on
Uranium (61)
Committee formed by Roosevelt in response to Leo Szilard's
letter; provided recommendations for nuclear research
Army Corps of Engineers (62,
63)
Oversaw plant construction and bomb assembly in the production
phase of the Manhattan project
Asharite School of Theology
(5)
Religious belief system formed by Islamic scholars studying Greek
and Indian atomism
Atomic Energy Commission
(68)
Organization which assumed control of the atomic program in
1947
Bell Labs (17) Research center at which Clinton Davisson and Lester Germer
confirmed the de Broglie hypothesis
Carnegie Foundation (62) Organization of which Vannevar Bush was president
Catholic Church (5) Religious organization which initially opposed atomism
CERN (46) Organization supporting the Large Hadron Collider
Clinton Engineer Works (63) Organization established by the Army Corps of Engineers; later
became Oak Ridge National Laboratory
Department of Energy (68) Established in 1977 by Jimmy Carter; currently manages the
National Laboratories
Emergency Committee of
Atomic Scientists (68)
Group founded by Albert Einstein in 1946 to promote peaceful
atomic applications
Energy Research and
Development Administration
(68)
Agency which partially replaced the Atomic Energy Commission in
1974
European Union (59) ITER member
Hanford Engineer Works (64) Housed the B Reactor, a plutonium generating reactor
International Atomic Energy
Agency (69)
Founded by United Nations in 1957; promotes peaceful use of
nuclear materials; prevents the proliferation of nuclear weapons
Lawrence Livermore National
Laboratory (59)
Site of the National Ignition Facility
Los Alamos (64) Also known as Site Y; research area constructed to bring together
scientists working on the Manhattan Project
Los Alamos Ranch School
(64)
Site of what would become Site Y
National Bureau of
Standards (61)
Organization directed by Lyman Briggs
National Defense Research
Committee (62)
Proposed by Vannevar Bush to oversee development of the
atomic bomb
National Institute of
Standards and Technology
(27)
Agency which regulates standards of measurements; defined the
second in terms of cesium 137's oscillating frequency
National Laboratory system
(68)
System of research centers established by the Atomic Energy
Commission in the post-war era
Nazi Party (61) Political party which took control of Germany in 1933
NIST (27) See National Institute of Standards and Technology
Nuclear Regulatory
Commission (68)
Agency that partially replaced the Atomic Energy Commission in
1974
Oak Ridge National
Laboratory (68)
Laboratory that grew out of the Clinton Engineer Works
Princeton (59) Site of the Tokamak Fusion Test Reactor
Project Y (63) Weapons development laboratory of the Manhattan Project; led
by J. Robert Oppenheimer
S-1 Committee (62) Subcommittee of the NRDC investigating uranium enrichment;
included Ernest O. Lawrence
Scientific Advisory Panel (67) Rejected a public demonstration of the nuclear bomb
Site Y (64) See Los Alamos
Stanford (27) Research university which supercooled rubidium to 50 trillionths
of a Kelvin in 2015
United Nations (69) Founder of the International Atomic Energy Agency
United States Army (62) Directed the construction of the atomic bomb
University of California,
Berkeley (62, 64)
University of Ernest O. Lawrence, J. Robert Oppenheimer, Hans
Bethe, Edward Teller
University of Chicago (51) School which hosted the world's first nuclear reactor
US Food and Drug
Administration (43)
Department overseeing food irradiation
People
Adolf Hitler (61) Chancellor of Germany; leader of the Nazi Party
Albert Einstein (13, 18, 25) Proposed quantization of light energy (1905); won 1921 Nobel
Prize for explaining the photoelectric effect; expressed doubts
about quantum theory to Max Born; theorized a fourth state of
matter with integer spin particles (1924)
Alvin Weinberg (68) Director of Oak Ridge National Laboratory; coined the term "Big
Science" to describe the National Laboratory system
Antoine Lavoisier (6) Late 1700s French chemist; identified and named hydrogen and
oxygen; theorized the law of conservation of matter
Aristotle (5) Third century BCE Greek philosopher; disagreed with atomism;
argued that matter is infinitely divisible
Arthur Compton (13, 62) American physicist; noted X-ray scattering in 1923, suggesting the
existence of the photon; asked J. Robert Oppenheimer to perform
neutron calculations for the uranium chain reaction; suggested
Oppenheimer as the director of Project Y
Arthur Eddington (56) English physicist; proposed stars produce energy through
hydrogen fusion
Carl Wieman (25) Created a Bose-Einstein condensate using laser cooling in 1995
Christiaan Huygens (9) Dutch physicist; contemporary of Newton’s; envisioned light as a
wave
Clinton Davisson (17) Researcher at Bell Labs; experimentally confirmed the de Broglie
hypothesis by firing electrons at crystalline nickel
Democritus (5) Fifth century BCE; early Greek philosopher; suggested that matter
is composed of indestructible, indivisible particles
Dmitri Mendeleev (6, 7) Nineteenth century chemist; created periodic table based on first
64 elements; predicted the existence of gallium
Donald Glaser (40) Invented the bubble chamber in 1952
Dwight D. Eisenhower (69) President of the United States; in 1953 delivered "Atoms for
Peace" speech to the United Nations
Edward Teller (57, 62) Hungarian-American physicist; conceived of and designed the first
hydrogen bomb; Berkeley "luminary" who worked with
Oppenheimer on neutron calculations for the atomic bomb
Emilio Segre (62, 65) Worked with Oppenheimer on neutron calculations; found that
products of X-10 reactor had too much plutonium-240 for a gun-
type bomb
Enrico Fermi (30, 37, 48, 51,
61)
Italian physicist after whom unit of nucleic radius is named; named
the neutrino; synthesized neptunium and plutonium; constructed
the first nuclear reactor at the University of Chicago in 1942; fled
to the United States during this period
Eric Cornell (25) Created a Bose-Einstein condensate using laser cooling in 1995
Ernest Marsden (7) Assistant to Ernest Rutherford in the gold foil experiment
Ernest O. Lawrence (62) Director of Radiation Laboratory at Berkeley; inventor of cyclotron
Ernest Rutherford (7, 30, 35,
57)
Performed 1911 gold foil experiment; discovered the nucleus;
theorized the neutron in 1920; proposed planetary atomic model;
proposed in 1900 that nuclear transformations release radiation;
experimentally demonstrated nuclear fusion in 1934
Ernest Walton (46) Irish physicist; in 1932, induced the first artificial nuclear reaction
with lithium-7
Erwin Schrödinger (19, 22) Austrian physicist; created equation describing behavior of matter
waves; described quantum behavior via scenario of cat in a box
Eugene Rabinowitch (68) Manhattan Project scientist; founded Bulletin of the Atomic
Scientists
Eugene Wigner (33) Proposed shell model for nucleons with Maria Goeppert Mayer
Felix Bloch (62) Worked with J. Robert Oppenheimer on neutron calculations
Franklin D. Roosevelt (62) President of the United States; approved initial research into an
atomic weapon; approved the NDRC
Frederic Curie (37) Husband to Irene Joliot-Curie; in 1934, demonstrated induced
radioactivity by generating radioactive phosphorous; won the
1935 Nobel Prize in Chemistry
Frederick Soddy (35) In 1900, concluded that nuclear transformations release radiation
with Ernest Rutherford
Fritz Strassman (48) German physicist; in 1938, discovered that bombarding uranium
nuclei with neutrons produced fission products with half
uranium’s mass
George Gamow (23) In 1940, wrote Mr. Tompkins in Wonderland
Gustav Hertz (16) In 1914, confirmed Bohr's model of the atom by firing electrons
through mercury gas in a vacuum
Hans Bethe (57, 62) In 1939, proposed the proton-proton chain and CNO cycle; won
the 1967 Nobel Prize; "luminary" who worked with Oppenheimer
on neutron calculations
Hans Geiger (7, 40) Assistant to Ernest Rutherford; performed the gold foil experiment
in 1911; recorded the results of the gold foil experiment in a dark
room; developed a radiation detector which uses a low-pressure
tube of inert gas
Harry Truman (66) Vice President to President Franklin D. Roosevelt; became
president in 1945 after Roosevelt died in office
Heinrich Hertz (12) In 1887 discovered the photoelectric effect
Henri Becquerel (34) French physicist; first observed spontaneous radiation emission
Henry Wallace (62) Vice President to President Franklin D. Roosevelt
Irene Joliot-Curie (37) Daughter of Marie Curie; in 1934, demonstrated induced
radioactivity by generating radioactive phosphorous; won the
1935 Nobel Prize in Chemistry
Isaac Newton (6, 9) 1700s - 1800s; advocated for the corpuscular theory in Opticks
J. Robert Oppenheimer (62,
63)
Researcher at the University of California, Berkeley; performed
neutron chain calculations for the atomic bomb; assembled a
team of "luminaries" to study neutron calculations; affiliated with
Communism through family members; became head of Project Y
J.D. Lawson (58) Proposed criteria for nuclear fusion to occur
J.J. Thomson (7, 12) Measured the mass of a cathode ray particle in 1897; discovered
the electron; proposed the plum pudding model of the atom;
determined that sparks produced by the photoelectric effect are
actually electrons
James Chadwick (31, 48) English physicist; in 1931 performed experiments with paraffin to
confirm the existence of the neutron
James Clerk Maxwell (9) Scottish physicist; devised the unified theory of electromagnetism
in the late 19th century; described light as oscillating electric and
magnetic fields
James Franck (16) In 1914, confirmed Bohr's model of the atom by firing electrons
through mercury gas in a vacuum
Jimmy Carter (68) President of the United States; established Department of Energy
Johann Balmer (14) Swiss mathematical physicist; in 1885 derives a mathematical
relation between the lines in hydrogen's spectrum
John Cockcroft (46) British physicist; in 1932, induced the first artificial nuclear reaction
with lithium-7
John Dalton (6) English chemist; combined discoveries of Lavoisier and Proust;
formulated the first atomic theory in A New System of Chemical
Philosophy; catalogued atomic weights
John Donne (65) English poet; inspired the name of the Trinity test
John Van Vleck (62) Worked with J. Robert Oppenheimer on neutron calculations
John von Neumann (65) Mathematician; in September 1943, proposed an implosion type
weapon design
John Wheeler (48) Colleague of Neils Bohr
Joseph Proust (6) French chemist; realized that elements react in fixed proportions
Kanada (5) Fifth century BCE Hindu philosopher; suggested that matter
contains indestructible, indivisible particles
Leo Szilard (48, 61, 66) Hungarian physicist; in 1933, hypothesized that a nuclear chain
reaction could become self-sustaining; fled to the United States; in
1939 wrote a letter under Einstein's name recommending the
United States research nuclear weapons; petitioned for a public
demonstration of the nuclear bomb
Leslie R. Groves (63) Army Corps of Engineers General; director of the Manhattan
Project from September 1942; appointed Oppenheimer as its lead
Lester Germer (17) Researcher at Bell Labs who experimentally confirmed the de
Broglie hypothesis by firing electrons at crystalline nickel
Leucippus (5) Fifth century BCE Greek philosopher; suggested that matter is
composed of indestructible, indivisible particles
Lewis Straus (68) Predicted that nuclear power would make electricity free; AEC
commissioner; sought to discredit Oppenheimer for opposing the
hydrogen bomb
Lise Meitner (48) Collaborated with Otto Hahn and Fritz Strassman
Louis de Broglie (17) French physicist; in 1924, suggested a relationship between a
particle's momentum and wavelength
Maria Goeppert Mayer (33) In 1949, proposed a shell model for nucleons with Eugene Wigner
Marie Curie (34) French-Polish physicist; discovered polonium with husband; won
1903 and 1911 Nobel Prizes; died from radiation exposure in 1934
Mark Oliphant (57, 62) Australian physicist; in 1934 experimentally demonstrated nuclear
fusion; represented the British atomic team in United States
Max Born (18, 20) Received a letter from Albert Einstein on his skepticism about
quantum theory; in 1926, proposed that the square of a wave
function is the particle's probability density
Max Planck (11) German physicist; proposed the quantization of atomic energy
Michael Faraday (7) Discovered that generating an electric voltage across a cathode
ray tube caused the positive end to glow
Niels Bohr (14, 16, 48) Danish physicist; modified the atomic model to explain
quantization of energy; postulated the correspondence principle
Otto Hahn (48) German physicist; discovered that bombarding uranium nuclei
with neutrons produced fission products half as heavy as uranium
Otto Robert Frisch (48) Collaborated with Otto Hahn and Fritz Strassman; coined "fission"
Paul Dirac (24) In 1928, derived a relativistic form of the Schrödinger equation,
incorporating the spin quantum number into quantum mechanics
Phillip Lenard (12) In 1900, noticed several contradictions between the photoelectric
effect and classical physics
Pierre Curie (34) French physicist; discovered polonium with his wife; researched
radioactivity
Pierre Gassendi (5) Renaissance-era priest; reconciled atomism with Catholic beliefs
Plato (5) Greek philosopher; viewed matter as consisting of four basic
elements; assigned geometric shapes to types of matter
Rene Descartes (6) Philosopher who debated Pierre Gassendi during the Renaissance
Robert Boyle (6) Eighteenth century founder of modern chemistry; proposed
corpuscular theory
Robert Serber (62) Worked with J. Robert Oppenheimer on neutron calculations
Satyendra Bose (25) Theorized fourth state of matter with integer spin particles
Seth Neddermeyer (65) Physicist; conducted theoretical work which led to the design of
an implosion type weapon
Stanislaw Ulam (57) Performed calculations for Edward Teller, contributing to the
design of the hydrogen bomb
Thomas Young (9) Noticed double-slit interference in 1803;
Vannevar Bush (62) American science administrator; president of Carnegie
Foundation; proposed and first chair of the NDRC
Wilhelm Roentgen (34) German physicist; discovered X-rays in 1895; won 1901 Nobel
Prize in Physics
Willard Libby (44) American physical chemist; in the 1940s developed carbon dating;
won the 1960 Nobel Prize in Chemistry
William Lawrence (68) New York Times journalist who coined the term "Atomic Age"
Wolfgang Pauli (24, 37) In 1925, suggested that no two electrons in an atom can share all
four quantum numbers; in 1930, theorized the neutrino
𝑅 = 𝑅0𝑒−𝜆𝑡 𝑅 =
𝑅0 =
𝜆 =
𝑁 =
𝑁0
𝑡 =
𝑡ℎ =
𝑁 = 𝑁0𝑒−𝜆𝑡
𝛥𝑁 = −𝜆𝑁Δ𝑡
𝑡ℎ =ln 2
𝜆
𝜆 =ℎ
𝑝
𝜆 =
ℎ = 6.626 × 10−34 𝑚2
𝑘𝑔⋅𝑠=
𝑝 =
1
𝜆= 𝑅𝐻 (
1
𝑚2−
1
𝑛2)
𝜆 =
𝑅𝐻 = 1.097 × 107 𝑚−1
𝑚 =
𝑛 =
Δ𝑥Δ𝑝 ≥ℎ
2𝜋
Δ𝑥 =
Δ𝑝 =
ℎ = 6.626 × 10−34 𝑚2
𝑘𝑔⋅𝑠=
𝐸 = 𝑛ℎ𝑓
𝐸 =
𝑛 =
ℎ = 6.626 × 10−34 𝑚2
𝑘𝑔⋅𝑠=
𝑓 =
𝐸 = 𝑚𝑐2
𝐸 =
𝑚 =
𝑐 = 3 × 108 𝑚
𝑠=
𝐸𝑛 =−13.6 𝑒𝑉
𝑛2
𝐸𝑛 =
𝑛 =
𝑟𝑏 = 𝑛2𝑎0
𝑟𝑏 =
𝑛 =
𝑎0 = 0.0529 𝑛𝑚 =
𝑟 = 𝑟0𝐴13
𝑟 =
𝑟0 = 1.2 × 10−15 𝑚
𝐴 =
𝑛𝜏 > 𝑘
𝑛 =
𝜏 =
𝑘 = 1014𝑠
𝑐𝑚3
𝑘 = 1016𝑠
𝑐𝑚3
𝑋𝑍𝐴 → 𝑌𝑍−2
𝐴−4 + 𝐻𝑒24
𝑋𝑍𝐴 → 𝑌𝑍+1
𝐴 + 𝑒− + �̅�
𝑛01 → 𝑝1
1 + 𝑒−
𝑋𝑍𝐴 → 𝑌𝑍−1
𝐴 + 𝑒+ + 𝑣
𝑈92238 → 𝑇ℎ90
234 + 𝐻𝑒24
𝐶614 → 𝑁7
14 + 𝑒− + �̅�
𝐵𝑒47 + 𝑒+ → 𝐿𝑖3
7 + 𝑣
𝐶614 ∗ → 𝐶6
14 + 𝛾
𝐻𝑒24 + 𝐴𝑙13
27 → 𝑃1530 + 𝑛0
1
𝑃1530 → 𝑆𝑖14
30 + 𝑒+
𝐻𝑒24 + 𝑁7
14 → 𝑂817 + 𝐻1
1
𝑝11 + 𝐿𝑖3
7 → 2 𝐻𝑒24
𝐻12 + 𝐿𝑖3
7 → 2 𝐻𝑒24
𝑛01 + 𝑈92
235 → 𝑋𝑒54140 + 𝑆𝑟38
94 + 2 𝑛01
𝑛01 + 𝑈92
235 → 𝐵𝑎56141 + 𝐾𝑟36
92 + 3 𝑛01
𝐻12 + 𝐻1
3 → 𝐻𝑒24 + 𝑛0
1 + 17.59 𝑀𝑒𝑉
2 𝐻12 → 𝐻𝑒2
3 + 𝑛01 + 3.27 𝑀𝑒𝑉
2 𝐻12 → 𝐻1
3 + 𝐻11 + 4.03 𝑀𝑒𝑉
2 𝐻11 → 𝐻1
2 + 𝑒+ + 𝑣 + 0.42 𝑀𝑒𝑉
𝐻11 + 𝐻1
2 → 𝐻𝑒23 + 𝛾 + 5.49 𝑀𝑒𝑉
2 𝐻𝑒23 → 𝐻𝑒2
4 + 2 𝐻11 + 12.86 𝑀𝑒𝑉
This year’s science practice test places slightly more emphasis on understandings of the atomic model
over nucleic reactions, with section I having 34% of questions against 26% and 24% for sections II
(atomic nucleus and radioactivity) and section III (nuclear fission and fusion) respectively.
Section I questions focus heavily on models of the atom, both classical and quantum; little appears
on foundational findings leading to the quantum model such as spectral lines, the de Broglie
hypothesis, wave-particle duality, and Schrödinger’s equation.
Section II also focuses on atomic structure, specifically of the nucleus. Few questions address gamma
decay, induced radioactivity, and radioactivity detection and effects – though this last topic offers
great recall questions, so know this material well. Section III almost completely skips over Q values
and the discovery of fission, while section IV omits the detonation mechanisms and Trinity Test
portions, both of which will likely appear on later tests.
As might be expected, section IV questions are much more factual. Those from other sections do
require some lateral thinking and analysis, for example question 13 on analogies to Planck’s
quantized energy states. The correct answer, B, can be identified quickly once you observe that only
books increase stepwise (you cannot add half a book to a bookcase). Question 24 requires you to
connect material from different sections of the guide; cathode rays stand out as not being part of
the typical electromagnetic spectrum but rather a type of emission.
No math needed for this test, but know the elements and reactions: for example, question 26 on the
uranium-238 decay series points to an important equation, as does question 37 on the three decay
chains’ products. The closest you will be to calculating anything is on question 33. Recall that doubly
magic implies both neutron and proton numbers are magic; i.e. their sum (A) is twice the magnitude
of a magic number. In this case, 20 x 2 = 40, option B. The more tricky questions that require you to
pay close attention are the substantial number on standards and notation (11, 41, 45, 46) as well as
chronology and “firsts” (2, 12, 17, 47, 48, 50). Quite a few questions came in the form of “who
discovered X?” or “what did the discovery of X enable?”, so pay attention where it appears in the
guide.
Lastly, two questions that may need some clarification: the phrasing of question 18 leaves it unclear
what it is asking about, and the distracters vary between criteria for the process to occur (A, C) and a
description of the process (B, D, E). The answer, B, is relatively straightforward – in this case, no hidden
meanings involved; just go with the choice that fits most closely with the term provided. For question
29, students with more general knowledge of the topic may know that though the guide does not
explicitly state so, the uncertainty principle is generalizable to other quantum properties that form
correlate pairs. The most well-known, and only one the guide discusses, is position and momentum.
