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).