Ch. 29- Nuclear Physics

terminology

-atomic number

-isotops

-atomic mass

-The periodic table has elements sorted by number of protons (𝑍), a.k.a. the atomic number. (*determine identity of element)

-Atoms with the same number of protons and different numbers of neutrons (𝑁) are called isotopes of that element

-The atomic mass number (𝐴) is the total number of nucleons in the nucleus of an atom. A is approximately the number of g/mol for the atom or it’s molar mass Mmol: 𝐴 = 𝑁 + 𝑍. (*table=average of isotopes)

• ex: He6=Mmol is 6g/mol

-The standard notation to identify different isotopes is: 𝑍/𝐴 𝑋, where 𝑋 is the chemical symbol from the periodic table.

-Note that a deficit of electrons will give the atom a net charge (*but not in this class?)

The Strong Force

-Binds the nucleus together and only acts in the nucleus

-Only effects nucleons. A nucleon is a particle found in a nucleus (proton or neutron)

-Short range: 3.0 fm or less. 1 fm = 1 femto-meter = 10-15 m

-Strongest of the 4 fundamental forces in the universe

-Only attractive! (*doesn’t repel)

size of nuclei

-where 𝑟0 = 1.2 fm and 1 fm = 1 femto-meter = 10-15 m

-most of an atom is empty space (why a photon would fly right through); nucelus small in comparison but very dense

-nucleus more dense than anything but a black hole, why need a lot of energy to hold the nucelus together; protons and nutreons packed tightly together

true or false: The nuclear density is roughly constant ≈ 2.3 × 1017 kg/m3

true! bc protons and neutrons roughly same mass, so A cancels out and just left w/ constants

neutrinos

-Italian for “tiny neutral one”

-Theorized to exist in 1930 to conserve momentum in some radioactive decays

-Experimentally discovered 1956.

-Symbol: 𝝂 𝟎 the lower-case Greek letter “nu”

-The anti-neutrino has the Symbol: 𝝂bar 𝟎

-Neutrinos have:

• a very small mass (𝑚𝜈 ≈ 1x10-37 kg)

• zero charge

• travel at about 99% the speed of light

• are NOT affected by the Strong Force

-They are hard to detect, since neutrinos travel very far (through the Earth and you for example) without interacting with any matter; harmless.

particles vs anti-particles

-same mass, opposite charge, opposite spin

-particles: neutron, proton +, electron -, photon

-anti-particles: neutron bar, proton -, electron +/”positroin”, photon bar

The Weak Nuclear Force

-transforms particles in the nucleus to make the nucleus more stable

-charge is convserved

-2 types of beta decay

• Neutron decay: can occur outside the nucleus; neutron turns into protron

• Proton decay: can only occur in a nucleus; proton turns into neutron

PET

-A use for positrons (anti-electrons, e+) : Positron emission tomography (PET)

-injected w/ short half-life radioactive material and edmits positrons → positrons hit electrons and send out photons (in opposite directions) → detector detects photons and their energy

-particle + anti-particle = annihilate (and edmit photons can detect; e- + e- → 2 photons)

Nuclear Stability for Z < 10

-If N and Z are equal; the nucleus is generally stable and is safe to ignore Coulomb repulsion (electric force) (*repulsion their but not significant/strong enough; stable isotope)

-For larger Z (above 10) Coulomb repulsion is not negligible

-ex picture: Particles in a box model for 12C (*stable bc same # of protrons and neutrons; 13C radioactive bc extra neutron)

-The Pauli exclusion principle permits two protons and two neutrons per level

*most things are radioactive

Nuclear Stability for Z > 10

-What is the effect of taking into account electrostatic repulsion on our diagrams?

-Answer: all energy levels for protons (including the ground state) are raised relative to the neutron levels

*repulsion of proton significant; highest energy in proton box; raise 1st proton level to neutron level; want same number of particles in highest level box