# Chap 42: Nuclear Physics

## Sections

| Sec | Topic |
|-----|------|
| 42-1 | [Discovering the Nucleus](42-1-discovering-the-nucleus.ipynb) |
| 42-2 | [Some Nuclear Properties](42-2-some-nuclear-properties.ipynb) |
| 42-3 | [Radioactive Decay](42-3-radioactive-decay.ipynb) |
| 42-4 | [Alpha Decay](42-4-alpha-decay.ipynb) |
| 42-5 | [Beta Decay](42-5-beta-decay.ipynb) |
| 42-6 | [Radioactive Dating](42-6-radioactive-dating.ipynb) |
| 42-7 | [Measuring Radiation Dosage](42-7-measuring-radiation-dosage.ipynb) |
| 42-8 | [Nuclear Models](42-8-nuclear-models.ipynb) |

## Review & Summary

:::{glossary}
Discovering the Nucleus
  **Rutherford scattering** of alpha particles from thin metal foils showed that the atom has a small, dense, positively charged nucleus. Most alpha particles pass through with small deflection; the few large-angle scatterings indicate a compact core containing most of the mass.

Some Nuclear Properties
  A nucleus has $Z$ protons and $N$ neutrons. The **mass number** is $A = Z + N$. The **atomic mass unit** is $1\,\mathrm{u} = 931.5\,\mathrm{MeV}/c^2$. The **binding energy** $E_b$ is the energy required to separate the nucleus into its nucleons:

  $$
  E_b = (\Delta m)c^2
  $$ (eq-42-binding)

  where $\Delta m$ is the **mass defect** (difference between the sum of nucleon masses and the nuclear mass). The **semi-empirical mass formula** describes how $E_b$ varies with $A$ and $Z$.

Radioactive Decay
  The number $N$ of undecayed nuclei decreases exponentially with time:

  $$
  N = N_0 e^{-\lambda t}
  $$ (eq-42-decay)

  where $\lambda$ is the **decay constant.** The **half-life** is $T_{1/2} = (\ln 2)/\lambda = 0.693/\lambda$. The **activity** (decay rate) is $R = \lambda N = -dN/dt$, measured in becquerels (Bq; 1 Bq = 1 decay/s).

Alpha Decay
  A nucleus emits an alpha particle ($^4\mathrm{He}$ nucleus). The **decay energy** $Q$ is the total kinetic energy released. **Quantum tunneling** through the Coulomb barrier explains how alpha particles escape despite having energy less than the barrier height.

Beta Decay
  **Beta-minus decay:** $n \to p + e^- + \bar{\nu}_e$. **Beta-plus decay:** $p \to n + e^+ + \nu_e$. **Electron capture:** $p + e^- \to n + \nu_e$. The neutrino (or antineutrino) is required to conserve energy, momentum, and lepton number.

Radioactive Dating
  **Carbon-14 dating:** Living organisms maintain a ratio $^{14}\mathrm{C}/^{12}\mathrm{C}$; after death, $^{14}\mathrm{C}$ decays (half-life 5730 years) and the ratio decreases. Other isotopes (e.g., uranium series) date older materials.

Measuring Radiation Dosage
  **Absorbed dose:** gray (Gy) = 1 J/kg of energy deposited. **Equivalent dose:** sievert (Sv) = Gy × RBE (relative biological effectiveness). **Activity:** becquerel (Bq) = 1 decay/s.

Nuclear Models
  **Liquid-drop model:** treats the nucleus as an incompressible fluid; explains fission and the semi-empirical mass formula. **Shell model:** nucleons occupy orbitals; explains **magic numbers** (2, 8, 20, 28, 50, 82, 126) and nuclear spin.
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