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<em>6C^{12}<em>6C, 13</em>6C^{13}</em>6C, 614C^{14}_6C).

  • Nuclear Radius: Approximated by the formula R=R<em>0A1/3R = R<em>0 A^{1/3}, where R</em>0=1.2×10−15R</em>0 = 1.2 \times 10^{-15} m and A is the mass number.

  • Subatomic Particles:

    • Electron: Charge = −1.602×10−19-1.602 \times 10^{-19} C, Mass = 9.1094×10−319.1094 \times 10^{-31} kg
    • Proton: Charge = 1.602×10−191.602 \times 10^{-19} C, Mass = 1.6726×10−271.6726 \times 10^{-27} kg
    • Neutron: Charge = 0, Mass = 1.6749×10−271.6749 \times 10^{-27} kg

Nuclear Forces

  • Strong Nuclear Force: Attractive force between protons and neutrons, stronger than electromagnetic force at short distances (~10−1510^{-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 (Δm\Delta m): Difference between the mass of the nucleus and the sum of the masses of individual nucleons.

    • Formula: Δm=Zm<em>p+(A−Z)m</em>n−M\Delta m = Zm<em>p + (A - Z)m</em>n - M, where Z is the number of protons, A is the mass number, m<em>pm<em>p is the mass of a proton, m</em>nm</em>n is the mass of a neutron, and M is the mass of the nucleus.

  • Binding Energy (BE): Calculated using Einstein's equation, BE=Δmc2BE = \Delta m c^2.

    • In MeV: BE=[Zm<em>p+(A−Z)m</em>n−M]×931.1 MeVBE = [Zm<em>p + (A - Z)m</em>n - M] \times 931.1 \text{ MeV}

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

Radioactivity

  • Definition: Spontaneous disintegration of unstable nuclei.

  • Types of Radiation:

    • Alpha ($\alpha$) Particles: Helium nuclei (24He^4_2He), low penetration, high ionization.
      • Decay: A<em>ZX→A−4</em>Z−2Y+24He^{A}<em>{Z}X \rightarrow ^{A-4}</em>{Z-2}Y + ^4_2He
    • Beta ($\beta$) Particles: Electrons or positrons, moderate penetration and ionization.
      • Decay: A<em>ZX→A</em>Z+1Y+β−+ν^{A}<em>{Z}X \rightarrow ^{A}</em>{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=N<em>0e−λtN = N<em>0 e^{-\lambda t}, where N is the number of nuclei at time t, N</em>0N</em>0 is the initial number of nuclei, and λ\lambda is the decay constant.

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

Nuclear Reactions

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

    • Example: 235<em>92U+1</em>0n→144<em>56Ba+89</em>36Kr+301n+200 MeV^{235}<em>{92}U + ^1</em>0n \rightarrow ^{144}<em>{56}Ba + ^{89}</em>{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: 41<em>1H→4</em>2He+2β++energy4 ^1<em>1H \rightarrow ^4</em>2He + 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.