chapter 30 the nucleus

Chapter 30 The Nucleus

Objectives

• 30.1 Determine the number of neutrons and protons in nuclides

• 30.1 Describe three forms of radioactive decay and solve nuclear equations

• 30.1 Define half life and calculate the amount of material and its activity remaining after a given number of half lives

Objectives

• 30.2 Describe the operation of particle detectors and particle accelerators

• 30.2 Define antiparticles and calculate the energy of y rays emitted when particles and their antiparticles annihilate one another

• 30.2 Describe the quark and lepton model of matter and explain the role of force carriers

The Nucleus

• Remember that the nucleus is comprised of the two nucleons, protons and neutrons.

• The number of protons is the atomic number.• The number of protons and neutrons together is

effectively the mass of the atom.

Mass and Charge of Atom

• Nuclear charge of the Atom is equal to the number of protons times the elementary charge ‘e’ (1.6x10-19 C)

• Proton/Neutron mass = 1.66x10-27 kg• This mass is equal to 1u (or amu)• Atomic Mass Unit (u) = 1 P or 1 N

Mass and Charge

• Atomic Number: Number of protons, in many calculations referred to as ‘Z’

• Mass Number: Number of protons + neutrons, in calculations referred to as A

• All elements have the same atomic number but differ in mass number

• Chemically neutral elements have equal protons and electrons

Atomic Mass on Periodic Table

• Is an average. No actual element has that mass– Average person in America has 1.99 arms– Atoms have masses that are whole number integers

• Carbon naturally occurs as carbon-12 (98.9%), carbon-13 (1.1%), and carbon-14 (trace amounts)

Isotopes

• Not all atoms of the same element have the same mass due to different numbers of neutrons in those atoms.

• 100 or so elements, 2000 or so Nuclides• There are three naturally occurring isotopes of

uranium:– Uranium-234– Uranium-235– Uranium-238

Isotopes

• Still have the same amount of protons and electrons, so have the same chemical properties

Practice Problems

• An isotope of oxygen has a mass number of 15. How many neutrons are in the nuclei of the isotope?

• How many neutrons does carbon-12, carbon-13, and carbon-14 have?

The Four Fundamental Forces

• In order of relative strength:• Strong• Electromagnetic• Weak• Gravitational

Strong Force

• Range: 10 x -15 m• Exchange particles: Gluons (g)• This force, through the presence of gluons,

holds quarks together.• Keeps Nucleus together

Electromagnetism

• Range: ∞• Exchange particles: Photon (γ)• This is the force that is a combination of

electricity and magnetism that governs the photon reactions of the entire universe instantaneously.

Weak Force

• Range: 10 x -17 m• Exchange particles: W+, W- and Zº• This allows quarks and leptons to change into

different types of themselves.

Gravity

• Range: ∞• Exchange particles: Graviton (Theoretical, not

yet proven to exist)• This is the attraction between two things of

mass.

The Unification of Physics

• Many people believe that all things in the Universe can be described by one equation that brings together the four fundamental forces.

• This is the quest to unify all of physics under one predictably accurate formula.

The Unification of Physics

• Many believe in a Big Bang theory.• In the first fractions of a second of the

Universe gravity split off followed by the strong force leaving those two and the electroweak force. Then the electroweak force split into the weak force and the electromagnetic force.

The Unification of Physics

• Many theories of this have come about including ones with strings that operate in 10 or 11 dimensions that are too small to affect us.

• For more info see: PBS’s program The Elegant Universe

Radioactivity

• It is not uncommon for some nuclides of an element to be unstable, or radioactive.

• We refer to these as radionuclides.• There are several ways radionuclides can

decay into a different nuclide.

Types ofRadioactive Decay

Alpha Decay:

Loss of an -particle (a helium nucleus)He4

2

U23892 Th234

90 He42 +

Beta Decay:

Loss of a -particle (a high energy electron)Neutron turns into Proton (emits electron)

0−1 e0

−1or

I13153 Xe131

54 + e0−1

Positron Emission:

Loss of a positron (a particle that has the same mass as but opposite charge than an electron) e0

1

C116 B11

5 + e01

Gamma Emission:

Loss of a -ray (high-energy radiation that almost always accompanies the loss of a nuclear particle)

00

Electron Capture (-Capture)

Addition of an electron to a proton in the nucleus– As a result, a proton is transformed into a neutron.

p11 + e0

−1 n10

Kinetics of Radioactive Decay

• Nuclear transmutation is a first-order process.

= kt Nt

N0

ln

Kinetics of Radioactive Decay

• The half-life of such a process is:

= t1/2 0.693

k• Comparing the amount of a radioactive

nuclide present at a given point in time with the amount normally present, one can find the age of an object.

Kinetics of Radioactive Decay

A sample of carbon initially has 15.2 grams of 14C. After some time, the amount of 14C is found to be 11.6 grams. The half-life of 14C is 5715 yr. How long has the sample been decaying?

Kinetics of Radioactive Decay

First we need to determine the rate constant, k, for the process.

= t1/2 0.693

k

= 5715 yr 0.693k

= k 0.6935715 yr

= k 1.21 10−4 yr−1

Kinetics of Radioactive Decay

Now we can determine t:

= -kt Nt

N0

ln

= -(1.21 10−4 yr−1) t 11.615.2ln

= -(1.21 10−4 yr−1) t ln 0.763

= t 2523 yr

Question

• 20 grams of an unknown isotope is found. After 3 hours, the sample only contains 17 grams of the isotope. What is the half life of the isotope?– Ln (Initial/Original) = - kt– -.163 = - k 3hrs– K = 0.0543– 0.693 / k = t.5– 12.75 hours

Question

• After 8 half lives, what fraction of the original isotope is left?

Stimulated Decay

• Done by nuclear bombardment

• Neutrons are uncharged, and not repulsed by nucleus, so used to stimulate decay

• Still, where do you get neutrons from? Need devices to cause things to run into each other…

Particle Accelerators

• In a linear accelerator, a series of hollow tubes are connected to a source of high frequency alternating voltages – Energy of proton increases by set amount at each

interval

Particle Accelerators

• A synchrotron is a particular type of cyclic particle accelerator in which the magnetic field (to turn the particles so they circulate) and the electric field (to accelerate the particles) are carefully synchronized with the traveling particle beam.

Large Hadron Collider

• This is the newest and best particle accelerator located in France and Switzerland. It is accessed by many research facilities all over the world via computer database sharing.

How much energy?

– The bigger the faster (Stanford’s is 3.3 km long)• Energies in the 1x1012 eV are reached– 1 eV = 1.6 x 10-19 Joules– Lots of energy for an electron or proton though

• How do we detect?– By the current, ionization of electrons from atoms– 100 GeV is plenty of energy to ionize even the

Helium with its measly 25 eV Ionization energy

Measuring Radioactivity

• One can use a device like this Geiger counter to measure the amount of activity present in a radioactive sample.

• The ionizing radiation creates ions, which conduct a current that is detected by the instrument.

Particle Physics

The Fundamental Building Blocks of the Universe

Current Understanding

What are quarks?

• The name “quark” is from a line in James Joyce’s book Finnegan’s Wake: “Three quarks for Muster Mark…”

• It was brought forth by physicist Murray Gell-Mann who created the quark model and showed their existence.

What are quarks?

• An atom is a nucleus of protons and neutrons with electrons moving around it.

• Inside each proton and neutron are smaller particles called quarks, three in each individual one.

What are quarks?

• There are 6 different flavors (types) of quarks: Up, Down, Strange, Charm, Bottom and Top.

What are quarks?

• The quarks have charges of either +2/3 or -1/3

What are quarks?

• Protons are made up of two Up quarks and one Down: (+2/3) + (+2/3) + (-1/3) = +1. A proton has a charge of +1.

• Neutrons are made up of one Up quark and two Down: (+2/3) + (-1/3) + (-1/3) = 0. A neutron has a charge of 0.

Anti-matter

– Each quark has an antiquark that corresponds to it: Top and Antitop, Charm and Anticharm, etc. and are denoted with this symbol above the letter: ū meaning Antiup.

• Each antiquark is the same number but opposite sign of its quark partner.

• Positron is anti-electron• Anti-matter eliminates the other matter

releasing energy

What are quarks?

• Each quark belongs to one of three generations:

• 1st Up and Down• 2nd Strange and Charm• 3rd Bottom Top• Generations are different due to the masses of

the particles. As generation grows, so does mass.

What are quarks?

• Quarks are impossible to isolate because the Strong force holds them together by way of exchanging gluons. Any isolated quark will immediately join another quark.

Baryons

• Baryons are any of the many combinations of three-group quarks.

Mesons

• Mesons are made up of any combination of a quark-antiquark pair.

Pentaquarks

• Pentaquarks have four quarks and one antiquark.

Hadrons

• Hadrons are the group that include all the Baryons, Mesons and Pentaquarks. Hadrons are any two, three or five quark (pentaquark) group.

Leptons

• The electron is apart of the group called leptons. These are particles with no known inner structure. There are also six of them:

1st 2nd 3rd

Leptons

• Each have antiparticles just like quarks. The positron, or the electron’s antiparticle, is emitted during β+ decay.

• Neutrinos are constantly hitting the Earth’s atmosphere from the Sun and go through neutrino oscillation in which they can be converted to any type of neutrino, Electron, Muon or Tau.

Mass of Generation 1 Particles

– Written in eV (mass is energy)• Up/Down Quark 330 MeV• Electron 0.511 MeV

Anti-matter revisited

• Back to Anti-matter… If an electron and positron come in contact, they have 0.511 MeV of energy(mass) and both are annihilated giving off 1.02 MeV of energy

• Pair Production can also occur. If a gamma ray of energy 1.02 MeV passes close to a nucleus, an electron and positron can be created• How we create the 2nd and 3rd generation particles