Radioactivity
Types of Radiation
Radioactive decay is spontaneous (happens without external cause) and random (cannot predict which nucleus will decay next).
| Property | Alpha (α) | Beta (β−) | Gamma (γ) |
|---|---|---|---|
| Nature | 42He nucleus | Fast electron | EM radiation |
| Charge | +2e | −1e | 0 |
| Ionising power | Strong | Moderate | Weak |
| Penetrating power | Paper / few cm air | Few mm aluminium | Several cm lead |
| Deflected by fields? | Yes (slight) | Yes (large) | No |
Inverse Square Law for Gamma
Gamma radiation intensity follows an inverse square law:
Radioactive Decay Equations
The number of undecayed nuclei decreases exponentially:
Activity A is the number of decays per second:
Half-life is the time for the number of undecayed nuclei to halve:
Worked Example
A sample has a half-life of 8.0 days. What fraction remains after 24 days?
Step 1: Number of half-lives = 24 / 8.0 = 3
Step 2: Fraction remaining = (½)3 = 1/8
Worked Example
A sample of 5.0 × 1018 atoms has λ = 7.62 × 10−10 s−1. Find the activity.
A = λN = 7.62 × 10−10 × 5.0 × 1018 = 3.81 × 109 Bq
Exam Tip
Remember: radioactive decay is random and spontaneous. You cannot speed it up or slow it down by changing temperature, pressure, or chemical state.
Nuclear Radius
Nuclear Radius Formula
The radius of a nucleus is given by:
where r0 ≈ 1.2–1.4 fm (1 fm = 10−15 m) and A is the nucleon number (mass number).
This shows that nuclear volume is proportional to A, which means nuclear density is approximately constant for all nuclei.
Worked Example
The nuclear radius of oxygen-16 is 3.0 fm. Estimate the radius of tin-120.
Step 1: Find r0 = R / A1/3 = 3.0 / 161/3 = 3.0 / 2.52 = 1.19 fm
Step 2: r(Sn-120) = 1.19 × 1201/3 = 1.19 × 4.93 = 5.9 fm
Electron Diffraction
High-energy electron diffraction is used to measure nuclear radii. Electrons are scattered by the nucleus and produce a diffraction pattern. The angle of the first minimum gives information about the nuclear size.
Key Facts
- Nuclear density ≈ 1017 kg m−3 — extraordinarily dense
- Nucleon number A = protons + neutrons
- The atom is mostly empty space; the nucleus is about 10−15 m across while the atom is about 10−10 m
Mass & Energy
Mass Defect & Binding Energy
The mass defect Δm is the difference between the total mass of the separate nucleons and the actual mass of the nucleus.
This “missing mass” has been converted into binding energy via Einstein's equation:
Binding energy is the minimum energy required to completely separate all nucleons in a nucleus. Higher binding energy = more stable nucleus.
Worked Example
Helium-4 has mass 4.0015 u. Calculate its mass defect and binding energy. (mp = 1.0073 u, mn = 1.0087 u)
Step 1: Total nucleon mass = 2(1.0073) + 2(1.0087) = 4.0320 u
Step 2: Mass defect = 4.0320 − 4.0015 = 0.0305 u
Step 3: Binding energy = 0.0305 × 931.5 = 28.4 MeV
Step 4: Binding energy per nucleon = 28.4 / 4 = 7.1 MeV
Binding Energy per Nucleon Curve
The graph of binding energy per nucleon against nucleon number is one of the most important diagrams in nuclear physics.
Binding energy per nucleon curve — Fe-56 is the most stable nucleus. Fusion releases energy for light nuclei; fission releases energy for heavy nuclei.
Key Facts
- Iron-56 has the highest binding energy per nucleon (≈ 8.8 MeV) — the most stable nucleus
- Energy is released when nuclei move towards higher binding energy per nucleon
- Light nuclei release energy by fusion; heavy nuclei release energy by fission
Fission, Fusion & Reactors
Nuclear Fission
A heavy nucleus (e.g. uranium-235) absorbs a neutron and splits into two lighter daughter nuclei, releasing energy and typically 2–3 neutrons. These neutrons can cause further fission, creating a chain reaction.
Nuclear fission chain reaction — each fission releases neutrons that cause further fission events
Nuclear Fusion
Two light nuclei combine to form a heavier nucleus, releasing energy. This is the process that powers stars.
Fusion requires extremely high temperatures (> 107 K) to overcome the electrostatic repulsion between the positively charged nuclei.
Nuclear Reactors
A fission reactor maintains a controlled chain reaction to produce thermal energy:
- Fuel rods: contain fissile material (e.g. enriched uranium-235)
- Moderator: slows fast neutrons to thermal speeds (e.g. water, graphite) — slow neutrons are more likely to cause fission
- Control rods: absorb neutrons to control the reaction rate (e.g. boron, cadmium) — raised to speed up, lowered to slow down
- Coolant: transfers thermal energy from the core to a heat exchanger (e.g. water, CO2)
- Shielding: thick concrete surrounds the reactor to absorb radiation
Safety & Waste
Nuclear waste is classified by activity level. High-level waste (spent fuel) remains radioactive for thousands of years and must be stored securely, typically in deep geological repositories. Intermediate and low-level waste require less stringent storage.
Key Facts
- Fission: heavy nucleus splits → lighter nuclei + neutrons + energy
- Fusion: light nuclei join → heavier nucleus + energy
- Both processes move nuclei towards higher binding energy per nucleon (towards Fe-56)
- Critical mass is the minimum amount of fissile material needed to sustain a chain reaction
Exam Tip
When explaining why energy is released, always refer to the binding energy per nucleon curve: the products have a higher binding energy per nucleon than the reactants, and the difference is released as kinetic energy.
Nuclear Physics Flashcards
Click to flip. Use arrow keys to navigate, space to flip.
Nuclear Physics Quiz
Test your knowledge of nuclear physics.
Nuclear Physics - Mock Exam Questions
Practice exam-style questions. Write your answer, then check the mark scheme.