Intro to Modern Physics

Light - Wave or Particle????

Is light only a wave?

• http://video.google.com/videoplay?docid=-4237751840526284618#

EXPERIMENTS THAT PROVE LIGHT’S A WAVE

Review - 19th Century

Interference - "Double Slit Experiment" - constructive/ destructive

• This was first shown in 1801 by Thomas Young, who sent sunlight through two narrow slits and showed that an interference pattern could be seen on a screen placed behind the two slits.

2) Polarization - "Filtering of Light -

• Un-polarized light is composed of light oscillating in all directions.

• Polarizers convert un-polarized light into polarized light that is parallel to the axis of the polarizer.

3) Diffraction - Spreading out of Light behind a barrier

4) Doppler - Color Shift of Light - "Blue to, Red Away"

EXPERIMENTS SUPPORTING PARTICLE THEORY OF LIGHT

(20th century)

Photoelectric Experiment

• Experiment in the late 1800's baffles scientists– light was not acting like a wave!

• - When light is exposed to the surface of certain metals, the light energy is absorbed and electrons are ejected

• http://www.stmary.ws/highschool/physics/home/animations3/modernPhysics/photoelectricEffect.swf

Photoelectric effect

Emitted electrons are called PHOTOELECTRONS

Light (or other electromagnetic radiation)

Photosensitive metal

The light’s energy causes the emission of electrons

Unexpected ResultsAs long as you are above a certain frequency

(threshold frequency, f0) ...• When you brighten the light source - Get

more electron emission

Rate of Photoelectronemission

Intensity of light (Brightness)

…

… BUT…not faster (more energetic) electrons!!!!

K.E. ofPhotoelectrons

Intensity of light (Brightness)

Kinetic Energy of Photoelectrons remains constant

Results contradict Wave Theory!

According to Wave Theory

• Increasing brightness, increases the energy of the wave

– Therefore - Should Increase Kinetic Energy of Electrons Emitted

• It Didn't!!

Black -Body Radiation and Planck’s Hypothesis

• When a solid is heated it emits electromagnetic radiation

• As the temp is increased, the radiation shifts toward shorter wavelengths– i.e. Heated solids glow red, then orange, and finally

white• Ideal black body or cavity radiator is a hollow

solid with a small opening drilled in one of the walls – used to study black-body radiation

What did they find?

• When solid was heated, the radiation emitted through the opening only depended on temperature not material

• Why?• Heating caused the atoms to oscillate and then

the energy was released as EM radiation• In 1900, Max Planck found that the atomic

‘oscillators’ can only have certain quantized energies

Photons and quantized energy

• In 1905, Albert Einstein published a theory explaining the photoelectric effect using quantum theory developed by Max Planck.

• Einstein said that light and other electromagnetic radiation consist of discrete, quantized bundles of energy – PHOTONS

• The energy of a photon depends on its frequency.

Energy of a Photon

• The energy of a quantum is given by the equation:E = h f = h c/λ

• E is in Joules• f is in Hz• Planck’s constant, h , is a universal constant

h = 6.63 x 10-34 Js• Small energy values of quanta are often expressed in

eV1eV = 1.60 x 10-19 J

homework

• In TEXT book• READ pgs 722-734• Do Practice problems 1-9 all

Einstein’s Photoelectric Equation

KEmax = hf – W• When a photon with energy hf strikes a

surface, a part of its energy (the work function, W) frees the electron from its bonds.

• Remainder energy gives electron its KE

Example

• A photon with frequency = 8.0 x 1014 hz strikes a photoemissive surface with work function = 1.7 x 10-19 J.

Calculate: (a) the maximum KE of ejected electrons

(b) the threshold frequency of the surface

Solution

(a) KEmax = hf – W= (6.63 x 10-34 Js)(8.0 x 1014 hz) – 1.7 x 10 -19 J= 3.6 x 10 -19 J

(b) The threshold frequency (f0) is the frequency at which KE of photoelectrons is zero. KEmax = hf – W = 0

So W = h f0 1.7 x 10 -19 J = (6.63 x 10 -34 Js) f0 f0 = 2.6 x 10 14 hz

THE COMPTON EFFECT2nd proof of photon theory

Compton effect

• Arthur Compton, a US physicist, bombarded a block of graphite with x-rays of known frequency

• He discovered that both electrons and x-rays emerged from the block as shown and found– Scattered x-ray freq, f’ < f , incident x-ray freq and both

energy and momentum were conservedGraphite block

Incident X-ray (frequency = f)

θ1

θ2

Scattered x-ray (frequency = f’)

Scattered electron(velocity = v)

Magnitude of momentum of a photon

• Photon‘s energy & momentum decrease equalsElectron's energy & momentum increase.

**Mass, energy, momentum is conserved. **p = E/c = hf/c = h/λ

Note: High frequency light (uv, x-rays, gamma radiation) behaves more like particles and less like waves;

Low frequency light (radio waves, microwaves, infrared radiation) behaves more like waves and less like particles

p = E/c = hf/c = h/λ

• Which color of light has the greatest momentum?

VioletHighest f, Smallest λ

example

• Calculate the momentum of an x-ray photon whose wavelength is 1.0 x 10 -10 meter

Solution p = h/λ = (6.63 x 10 -34 Js) / (1.0 x 10 -10 m)

= 6.6 x 10 -24 kg m/s

Matter Waves

• In 1924, French Physicist, Louis De Broglie, stated that nature was symmetrical and that

p = mv = h/λshould hold for both light and matter.p = momentum of the particleλ - called DeBroglie Wavelengthh - Planck's constant

The waves associated with matter, matter waves, do not behave as other waves in that they do not travel in space

Matter waves

• The wavelength of ordinary objects are insignificant because their masses are too large.BUT…

• Electrons are small enough to have wave behavior.

• 1927- Diffraction and interference patterns were observed for electrons. – A scientist passed electrons through tiny double

slits and observed interference patterns

example

• Calculate the wavelength of a proton whose speed is 5.0 x 10^6 m/s

Solutionp = mv = h/λλ = h = ( 6.6 x 10 -34 Js) .

(mv) (1.66 x 10 -27 kg)(5.0 x 10 6 m/s) = 8.0 x 10 -14 m

Summary

• Light behaves like a wave in interaction with large objects and like particle with very small objects like electrons

Early models of the atom

http://www.montereyinstitute.org/courses/AP%20Physics%20B%20II/course%20files/multimedia/lesson52/lessonp.html

• An atom is the smallest particle of an element that retains the characteristics of the element.

• An atom contains protons, neutrons, and electrons.

• Protons have a positive charge.• Electrons have a negative charge.• Neutrons have no charge. (They are

neutral.)

What is an Atom?

• Thomson discovered that electrons have a low mass, and that there is such a thing as a negative charge.

• He concluded that because there is a negative charge, there must be a positive charge in order for an atom to be neutral.

• Thought an atom consisted of a uniform distribution of positive charge in which electrons are embedded like plums in a pudding.

Thompson’s Model of the Atom

Thompson’s Plum Pudding Model

Ruther fo rd ’s Mode l• Earnest Rutherford proposed another model of the

atom.• He directed a beam of massive, positively charged

particles at extremely thin gold foil.• A small number of particles were scattered throughout

the foil at large angles• this concentration of mass and positive charge in the

atom is located at the atom’s center (nucleus).

particles

gold foil

detector

http://www.stmary.ws/highschool/physics/home/notes/modPhysics/early_models_of_atoms.htm

• He concluded that the nucleus is only 1/10,000 the diameter of the average atom.

• He described the atom as being a miniature solar system; the nucleus being the center where all positive charges are contained, and the outer surroundings include the electrons.

• The electrons move in orbits around the

nucleus and are held in orbit by Coulomb forces of attraction between their negative charges and the positive charge of the nucleus.

Did you know ...

• If the atom were the size of a football stadium, the nucleus would be the size of a....

• Marble !!!!!

• That's why most alpha particles go straight through!!!

Did you know ...

• A neutron star is created when a massive star runs out of fuel and collapses. This tremendous gravitational collapse squeezes all the empty space out of the atom. Electrons merge with protons and create neutrons.

• The density of a neutron is so enormous that a teaspoon of a neutron star would weigh 20 billion pounds!!!

Can’t be explained using Rutherford’s Model

1. Orbiting electrons are accelerating charges and thus should produce electromagnetic radiation. This release of energy should cause electron’s orbit to decrease leading to the collapse of atoms. But atoms are STABLE

2. When heated or subjected to high potential differences, atomic gases (ex. hydrogen), produce light emission spectra, rather than continuous emissions like a rainbow. WHY?

Line emission Spectra

• The diagram below represents a partial line spectrum (in the visible light region).

• Note: The wavelengths are in nanometers.

Niels Bohr

• Early 1900's - Danish scientist Neils Bohr discovers the strange behavior of electrons.

• Tried to explain why electrons were able to maintain their positions outside the nucleus rather than spiral into the nucleus and cause the atom to collapse.

The Bohr Model• In the Bohr Model the neutrons

and protons (symbolized by red and blue balls in the adjacent image) occupy a dense central region called the nucleus, and the electrons orbit the nucleus much like planets orbiting the Sun (but the orbits are not confined to a plane as is approximately true in the Solar System).

• Electrons in atomsare restricted in the energies they can possess, give off and absorb.

Bohr proposed

• That the hydrogen atom possesses distinct orbits• At any instant, the single electron of hydrogen

can be associated with one and only one orbit.• Each orbit gives the hydrogen atom a specific

amount of energy (Bohr called these energy levels)

• Energy levels are identified by integers – Quantum Numbers

Definitions Atom• Stationary state: when an electron

is in a particular orbit• Energy level: a specific amount of

energy • Ground state: when an electron is in

its lowest energy level• Excited state: an electron in any

level above the ground state

• Excitation: any process that raises the energy level of electrons in an atom– Can be the result of absorbing the energy

of colliding particles of matter– Excitation energies are different for

different elements •Atoms rapidly lose the energy of their various excited states as their electrons return to the ground state• Ionization potential: the energy required to remove an electron from an atom to form an ion

Energy Levels

Bohr’s emission calculations

2

6.13neVEn

Example: Calculate the energy of a hydrogen atom when its electron is associated with energy level2

eVeVE

neVE

Solution

n

40.326.13

6.13:

22

2

If n is considered infinitely large, the energy of the hydrogen atom is taken to be zero because the electron is no longer considered to be associated with the atom – ionization.

The reference table has these calculated already

• ΔE = Efinal – Einitial

• If ΔE is a negative number, the energy is emitted;

• If it is positive, the energy is absorbed

• The frequency of the photon that is emitted (or absorbed)can be calculated by …

• ΔE = hf

Energy Level Diagram for a

Mercury atom •Notice spacing is more complex and less regular than hydrogen.•The Bohr model cannot be applied•However, we can calculate the energy of an electron transition between states

E = Ei - Ef

• Atomic Spectrum: the product of when electrons in excited atoms of an element in the gaseous state return to lower energy states

• Each element has a different spectrum, and is used as the “DNA” of the element

SPECTRA

To identify an unknown element

- Electrify, Heat it up and analyze its colors.

- Compare emitted colors to a database of elemental spectral lines

January 2006: The diagram below represents the bright-line spectra of four

elements, A, B, C, and D, and the spectrum of an unknown gaseous sample.

Based on comparisons of these spectra, which two elements are found in the unknown sample?

B & C

Bohr’s conclusions

1. Permitted orbits of an electron in an atom are limited2. Each orbit is a different energy3. Inside orbits have lower energies than the outside ones4. When electrons in an atom change energy states they

absorb or release energy • Up energy level, energy absorbed

• Down energy level, energy released as light

• A single photon of energy is given off when electrons go down energy levels.

More examples on line

• http://www.stmary.ws/highschool/physics/home/notes/modPhysics/bohr_atom_examples.htm

The Cloud Model

• Current model of the atom able to explain the structure of all of the atoms in the Periodic Table.

• Uses Quantum Mechanics to describe the probability of finding an electron

• Quantum Mechanics does not place electrons in specific orbits – complicated equations describe the shape, location and density of each electron cloud in an atom.

• Electron Cloud: The most probable regions of the electron’s location

The Nucleus

The Nucleus

• After Ernest Rutherford proposed his nuclear model, physicists began to question whether the nucleus had a structure of its own.

• There is still no complete answer to this question.

• However in the mid 1930s, a simple nuclear model was in place.

Nucleons

• The components of the nucleus are called nucleons and are described by a number of properties including electric charge.

• Nuclear charge is measured by elementary charge(e) rather than the coulomb.

• Two principal nucleons are the proton and the neutron.

Nuclear symbols• All atomic nuclei and their components

nucleons are represented by the same general symbol

• The symbol identifies the particle (Au), atomic number, indicates the number of elementary charges present(79 protons), and the mass number, is equal to the sum of neutrons and protons (197)

Symbols

# of Neutrons = Mass Number – Atomic NumberFor Gold (Au) N = 197 – 79 = 118

Symbols for proton, neutron, and electron

(electron) (neutron) (proton) 0-1

10 enH11

Isotopes

• Atoms that have the same atomic number but have different mass numbers

• All atoms of the same element have the SAME number of PROTONS

• However, isotopes have DIFFERENT number of NEUTRONS

• Ex: Hydrogen, Deuterium,and Tritium

Nuclear Masses

• Measured in Atomic Mass Unit (u) rather in kg• AMU: 1u = 1.66 x10-27 kg• Mass of proton = 1.0073 u; • Mass of neutron = 1.0087 u• Mass of electron = 0.0005 u.• Isotope carbon-12 – basis for the nuclear-mass

scale – one carbon-12 atom is assigned an exact mass of 12 amu

Mass – Energy Relationship

• Nuclear masses may be expressed in terms of their energy equivalents

• Einstein showed that mass and energy are equivalent

E = mc2

Calculate the energy equivalent of 1 atomic mass unit in joules and in Mev

Calculate the energy equivalent of 1 atomic mass unit in joules and in Mev

Solution: first in joules E = mc2

Need the following:Mass: 1u = 1.66 x10-27 kg C = 3.00 x 108 m/sSubstituting in

E = (1.66 x10-27 kg)( 3.00 x 108 m/s)2

= 1.49 x 10-10 J

Calculate the energy equivalent of 1 atomic mass unit in joules and in Mev

Solution: Now in Mev Need the following: 1eV = 1.60 x10-19 J 1 Mev = 106 eVSubstituting in

eVxJx

eVx 819

10 1031.91060.111049.1

E•

MeVeV

MeVeVx 9311011031.9 6

8

Masses and energy equivalents of some nuclear particles

Particle Mass (u) Energy Equivalent

(Mev)Electron 0.0005486 0.5110Proton 1.007276 938.3Hydrogen (1 atom)

1.007825 938.8

Neutron 1.008665 939.6

Strong Nuclear Force• Positively charged protons in any nucleus containing more than

one proton are separated by a distance of 10-15 meter• Large repulsive Coulomb force exists, the gravitational force of

attraction is too weak to counterbalance this electrostatic repulsive force.

• How is nucleus able to stay intact?• STRONG NUCLEAR FORCE – 100 times stronger than

electrostatic force ; Strongest force known to exist!• At distances greater than a few nucleon diameters, the strong

force diminishes rapidly and becomes much less than gravitational and electrostatic forces.

Mass Defect and Binding Energy

• The mass of the atomic nucleus is less than the sum of its individual nucleon when measured separately (mass defect)

• Why?• The binding energy of a nucleus is the amount

of energy that must be added in order to separate the nucleus into its component nucleons

problem• Compare the mass of a nucleus (mass = 55.9206 u)

with the total mass of its nucleons. What’s the energy equivalent?

26 protons = 26 x 1.0073u = 26.1898u30 neutrons = 30 x 1.0087u = + 30.2340u total 56.4238u

- actual mass - 55.9206u 0.5032u

From ref table: 1 universal mass unit = 931 Mev

Fe5626

MeVuMeVxu 5.468

11031.95032.0

2

Modern Physics

Introduction• To examine the fundamental nuclear model• To examine nuclear classification• To examine nuclear fission and fusion

Detection Devices

• Geiger counter• Scintillation counter• Cloud chamber• Bubble chamber• Superheated liquid

Fundamental Particles • Democritus introduced the word which in

English translates as atom • Elementary Particles

– The name given to protons, neutrons and electrons

• Today we use the term "fundamental" for the six types of quarks and the six leptons

Classification of Matter• Hadrons: Particles made of quarks. Protons,

Neutrons and their Anti-particles• Leptons: Are NOT made of sub particles. Electrons

are examples of Leptons• Hadrons are further broken into Baryons and

Mesons. ( both break down into Quarks)

Hadrons• Hadrons break down into two groups

–Baryons are made of 3 Quarks –Mesons made up of 2 quarks and

anti-quarks***(must add up to an integer not a

fraction)

Leptons• Leptons are fundamental particles that have no

strong interactions

• Lepton is Greek for "light particle”• electron there are heavier leptons, of which the first

to be found was the muon • The TAU is 12th (quarks + leptons) fundamental

building blocks of all matter.

Quarks• Quarks are fundamental matter particles that

are constituents of neutrons and protons and other hadrons

• Proton -- composed of two Quarks up quarks and a down quark

Sample Problem• A Baryon may have a charge of

– -1/3e– 0e– +2/3e– +4/3e

• Correct answer is 0e (all types of matter must have an integer charge)

Scale of nature

• Particles are classified by size and charge

• Forces give all matter their characteristics and properties

Neutrinos (type of Lepton)

• These particles are so small that they pass right through the Earth without interacting with a single atom!!!

Four fundamental interactions

• Force : the effect on particle due to another particle

• Interaction: the forces and decays which affect a given particle

Strong Force• Quarks and Gluons have a type of charge that

is NOT electromagnetic• The “color” charged particles are very

powerful (STRONG)• Quarks are glued together with GLUONS

(Nuclear Energy)

Weak Force• The stable matter of the universe is made up

of the two least massive quarks: UP and Down and the least massive Lepton, the electron ( A Hydrogen Atom)

• When a quark or lepton changes type (muons changing to an electron) is called a “flavor” weak interaction

The components of the nucleus are called nucleons.

The two principle nucleons are the proton with a charge of +1e and the neutron which is uncharged.

All atomic nuclei (nuclides) and their components may be represented by the symbol below.

X is the name of the particle

A is the mass #

Z is the atomic #

XAZ XAZ

XAZ

Chemistry Symbols

IsotopesNuclei that have the same atomic number, but

different mass numbers.

HydrogenDeuterium Tritium

Nuclear ReactionRepresented by a balanced nuclear equation

HeCHN 42

126

11

157

Nuclear Fission & Fusion

• Fission is the chain reaction splitting of an atom

• Fusion is the joining of light nuclei to form a heavier more stable nuclei

Reference Chart : Standard Model

Reference Chart

Reference Chart Equations

• Ephoton = hf = hc/wavelength

• Ephoton = Ei – Ef

• E = mc2

• All equations calculate the amount of energy in units of eV or J. The conversion is based on the energy of a single electron or mass

Sample Problem• Calculate the energy of the photon that is

emitted when a hydrogen atom changes from energy level n=3 to 2

• Ephoton = Ei – Ef

• = (-3.40 eV) – (-1.51 eV)• = - 1.89 eV

Sample Problem• What is the Radiant energy of a beam of light

whose frequency is 5.0 x 1014 Hz• Ephoton = hf = hc/wavelength• = 6.6 x 10-34 J*s (5.0 x 1014 Hz)• = 33 x 10 -20 J

Summary• Atomic Particles are composed of sub-nuclear

particles• The nucleus is a conglomeration of Quarks

which manifest as Protons and neutrons• Each elementary particle has a corresponding

anti-particle• The fundamental source of energy is the

conversion of mass into energy