Nuclear Physics Notes

Nuclear Structure

  • Nucleus: Dense region with nucleons (protons and neutrons).

  • Nucleons: Protons (positive charge) and neutrons (no charge).

  • Atomic Number (Z): Number of protons.

  • Isotopes: Same number of protons, different number of neutrons.

  • Nuclide Notation: ^{A}_{Z}X where X is the element, Z is the atomic number, and A is the mass number.

  • Isotopes: Nuclides with same number of protons.

  • Isobars: Nuclides with same mass number.

  • Isotones: Nuclides with the same number of neutrons.

  • Isomers: Compounds with the same molecular formula but different structure.

  • Atomic Mass Unit (AMU): 1 amu = 1.66054 x 10^{-27} Kg = 931.49 MeV.

  • Nuclear Magnetons (µN): µN = eh/4πmp where mp is the proton mass.

Nuclear Size

  • Nuclear Radius: R = R0 A^{1/3}, where R0 = 1.25 x 10^{-15} m.

Nuclear Binding Energy

  • Binding Energy Formula: ΔE = Δmc^2 = (Zmp + Nmn – Mnuc)c^2

Nuclear Models

  • Liquid Drop Model: Nucleus as an incompressible liquid drop.

    • Accounts for volume, surface, Coulomb, asymmetry, and pairing energies.

    • Semi-empirical mass formula: m = Zmp + (A-Z)mn - EB/c^2

  • Shell Model: Nucleons arranged in energy levels based on the Pauli principle, leading to greater stability with filled shells.

  • Magic Numbers: 2, 8, 20, 28, 50, 82, 126 (more tightly bound).

  • Energy levels obtained by solving the Schrodinger equation.

Radioactive Decay

  • Decay Law: N = N_0 e^{-λt}, where λ is the decay constant.

  • Half-life: T_{1/2} = ln(2)/λ = 0.693/λ

  • Activity: |dN/dt| = λN

Types of Radioactive Decay

  • Alpha Decay: Emission of an alpha particle (^4_2He).

  • Beta Decay:

    • Beta-minus (β^−): Neutron converts to proton, emitting an electron and antineutrino (n → p + e^- + \bar{ν}).

    • Beta-plus (β^+): Proton converts to neutron, emitting a positron and neutrino (p → n + e^+ + ν).

  • Electron Capture: Proton captures an electron, converting to a neutron (p + e^- → n).

  • Gamma Decay: Emission of a gamma ray photon.

Radioactivity

  • Natural Radioactivity: Spontaneous nuclear reactions.

  • Artificial Radioactivity: Induced nuclear reactions by bombarding nuclei with particles.