Nuclear Physics Notes

Nuclear Physics

Key Concepts

  • Nuclear Physics: Study of the atomic nucleus, its structure, and the forces holding it together.

  • Atomic Nucleus: Consists of protons (positive charge) and neutrons (neutral charge), collectively called nucleons.

  • Isotopes: Atoms with the same number of protons but different numbers of neutrons (e.g., ^{12}6C, ^{13}6C, ^{14}_6C).

  • Nuclear Radius: Approximated by the formula R = R0 A^{1/3}, where R0 = 1.2 \times 10^{-15} m and A is the mass number.

  • Subatomic Particles:

    • Electron: Charge = -1.602 \times 10^{-19} C, Mass = 9.1094 \times 10^{-31} kg
    • Proton: Charge = 1.602 \times 10^{-19} C, Mass = 1.6726 \times 10^{-27} kg
    • Neutron: Charge = 0, Mass = 1.6749 \times 10^{-27} kg

Nuclear Forces

  • Strong Nuclear Force: Attractive force between protons and neutrons, stronger than electromagnetic force at short distances (~10^{-15} m).

  • Weak Nuclear Force: Responsible for radioactive decay.

Nuclear Binding Energy

  • Definition: Energy required to separate a nucleus into its constituent protons and neutrons.

  • Mass Defect (\Delta m): Difference between the mass of the nucleus and the sum of the masses of individual nucleons.

    • Formula: \Delta m = Zmp + (A - Z)mn - M, where Z is the number of protons, A is the mass number, mp is the mass of a proton, mn is the mass of a neutron, and M is the mass of the nucleus.

  • Binding Energy (BE): Calculated using Einstein's equation, BE = \Delta m c^2.

    • In MeV: BE = [Zmp + (A - Z)mn - M] \times 931.1 \text{ MeV}

  • Binding Energy per Nucleon: BEN = \frac{BE}{A}

Radioactivity

  • Definition: Spontaneous disintegration of unstable nuclei.

  • Types of Radiation:

    • Alpha ($\alpha$) Particles: Helium nuclei (^4_2He), low penetration, high ionization.
      • Decay: ^{A}{Z}X \rightarrow ^{A-4}{Z-2}Y + ^4_2He
    • Beta ($\beta$) Particles: Electrons or positrons, moderate penetration and ionization.
      • Decay: ^{A}{Z}X \rightarrow ^{A}{Z+1}Y + \beta^- + \nu
    • Gamma ($\gamma$) Rays: High-energy photons, high penetration, low ionization.

  • Ionization and Penetration: Gamma > Beta > Alpha in penetration; Alpha > Beta > Gamma in ionization.

  • Radioactive Decay Law: N = N0 e^{-\lambda t}, where N is the number of nuclei at time t, N0 is the initial number of nuclei, and \lambda is the decay constant.

  • Half-Life (t{1/2}): Time for half of the radioactive nuclei to decay; t{1/2} = \frac{0.693}{\lambda}.

Nuclear Reactions

  • Nuclear Fission: Splitting of a heavy nucleus into smaller nuclei.

    • Example: ^{235}{92}U + ^10n \rightarrow ^{144}{56}Ba + ^{89}{36}Kr + 3 ^1_0n + 200 \text{ MeV}

  • Nuclear Fusion: Combining two or more light nuclei into a heavier nucleus. Source of energy in stars.

    • Example: 4 ^11H \rightarrow ^42He + 2 \beta^+ + \text{energy}

Radiation Safety

  • Minimize Exposure: Reduce time, maximize distance, use shielding (lead, concrete, water).

  • Safety Measures: Proper handling with tongs/forceps, arm's length distance, eye protection.

Applications

  • Medical: Cancer treatment (radiotherapy), diagnostic imaging.

  • Radioactive Dating: Determining age of fossils and artifacts using isotopes like Carbon-14.

  • Energy Production: Nuclear reactors (fission), potential for fusion reactors.