Nuclear Physics Notes

Nuclear Physics

• Understanding the strong nuclear force led to the discovery of subatomic particles, requiring the reconciliation of quantum mechanics and special relativity.
• Nuclear and radiation physics explain phenomena from smoke detectors to star evolution.

Atomic Number (Z)

• $Z$ is the number of protons in the nucleus.
• In a neutral atom, the number of protons equals the number of electrons.
• Electron configuration determines chemical properties, thus chemical properties depend on $Z$.
• Elements are defined by $Z$.

Atomic Mass Number (A)

• $A$ is the total number of protons and neutrons (nucleons).
• An element $X$ is written as $^A_Z X$ for example $\ _{92}^{235}U$

Definitions

• Nucleon: A nuclear constituent (proton or neutron).
• Nuclide: A nucleus or atom with a specific nuclear makeup.
• Isotopes: Atoms with the same number of protons but different numbers of neutrons.
• Isotones: Atoms with the same number of neutrons but different numbers of protons.
• Isobars: Atoms with the same number of nucleons but different numbers of protons.
• Isomers: Atoms with the same number of protons and neutrons but different nuclear energy states (e.g., $\ ^{m}Xe$).

Atomic Mass Unit (amu)

• Defined such that the atomic mass of Carbon-12 is exactly 12 amu.
• Avogadro’s Number is the number of atoms in exactly 0.012 kg of Carbon-12.
• $1 \text{ amu} = 1.66 \times 10^{-27} \text{ kg}$.

Energy Equivalent of Mass

• Using $E = mc^2$, $1 \text{ amu} = 931.494 \text{ MeV}$.

Strong Nuclear Force

• Short-range attractive force between nucleons; holds the nucleus together.
• The strongest of all forces, approximately 100 times stronger than electrostatic forces.
• Overcomes electrostatic repulsion between protons.

Binding Energy

• The mass of an atom's constituents is greater than the mass of the atom itself.
• Mass defect ($\Delta m$): The difference between the mass of the atom and its constituent parts.
• Binding energy is the energy required to break the atom into its constituents.
• Greater binding energy implies a more stable atom.

Stability Diagram (Segrè Chart)

• Graph of neutron number (N) vs. proton number (Z).
• Stable nuclei reside within a band; larger nuclei require more neutrons to overcome proton repulsion.

Nuclear Reactions

• Nuclear Decay
• Nuclear Fusion: Joining smaller nuclei to form larger nuclei (mass number < 56).
  • Requires extremely high temperatures ($\sim 10^9 \text{ K}$).
• Nuclear Fission: Breaking up larger nuclei to form smaller nuclei (mass number > 56).