6.1 Radioactive Decay
1. Radioactive Decay and Radiation
Radioactive decay is a spontaneous and random process in which an unstable nucleus emits ionizing radiation (alpha particles, beta particles, or gamma rays) to become more stable.
- Spontaneous: Not triggered or affected by external conditions such as temperature, pressure, or chemical reactions.
- Random: Impossible to predict which specific nucleus will decay at any given instant.
2. Types of Radioactive Radiation
- Alpha ($\alpha$) particle: Helium nucleus ($^{4}_{2}\text{He}$), high ionizing power, low penetrating power (stopped by paper).
- Beta ($\beta$) particle: High-speed electron ($^{0}_{-1}e$), medium ionizing power, medium penetrating power (stopped by a few mm of aluminium).
- Gamma ($\gamma$) ray: High-frequency electromagnetic wave ($^{0}_{0}\gamma$), low ionizing power, high penetrating power (stopped by thick lead or concrete).
3. Half-Life ($T_{1/2}$)
Half-life is the time taken for half the total number of unstable nuclei in a sample to decay, or for the activity of a radioactive sample to reduce to half its initial value.
$$N = N_0 \left(\frac{1}{2}\right)^n \quad \text{where } n = \frac{t}{T_{1/2}}$$
- $N_0$ = Initial activity / initial number of nuclei
- $N$ = Remaining activity / remaining number of nuclei
- $n$ = Number of half-lives elapsed
- $t$ = Total elapsed time
6.2 Nuclear Energy
1. Atomic Mass Unit ($\text{u}$) and Mass Defect ($\Delta m$)
$1\text{ atomic mass unit (u)} = 1.66 \times 10^{-27}\text{ kg}$.
Mass Defect ($\Delta m$): The difference between the total mass of individual nucleons before reaction and the total mass of products after nuclear reaction.
$$\Delta m = \sum m_{\text{reactants}} - \sum m_{\text{products}}$$
2. Nuclear Energy Equation ($E = mc^2$)
According to Einstein's Principle of Mass-Energy Equivalence, mass defect is converted into nuclear energy:
$$E = \Delta m \, c^2$$
- $E$ = Nuclear energy released ($\text{J}$)
- $\Delta m$ = Mass defect ($\text{kg}$)
- $c$ = Speed of light in vacuum ($3.0 \times 10^{8}\text{ m s}^{-1}$)
3. Nuclear Fission vs. Nuclear Fusion
- Nuclear Fission: Splitting of a heavy unstable nucleus (e.g., Uranium-235) into two lighter, more stable nuclei when struck by a slow neutron, releasing massive energy and additional neutrons (triggering a chain reaction).
- Nuclear Fusion: Combining of two light, small nuclei (e.g., Deuterium and Tritium) at extremely high temperatures and pressures to form a heavier nucleus (e.g., Helium), releasing tremendous energy. Fusion is the primary source of solar energy.
6.3 Nuclear Energy Generation in Reactors
1. Key Components of a Nuclear Fission Reactor
- Uranium Fuel Rods: Releases heat energy via nuclear fission chain reactions.
- Moderator (Graphite / Heavy Water): Slows down fast neutrons so they can be absorbed effectively by Uranium nuclei.
- Control Rods (Boron / Cadmium): Absorbs excess neutrons to regulate or stop the rate of nuclear reaction.
- Coolant (Water / Liquid Sodium): Absorbs and transfers thermal energy from reactor core to heat exchanger to generate steam.
- Concrete Shielding: Heavy lead or concrete wall that absorbs dangerous gamma radiation and leakage.