Nuclear Physics
Explore the nucleus of the atom — how radioactive elements decay, what half-life means, and the immense energy released by nuclear fission and fusion.
The Nucleus and Radioactivity
The nucleus of an atom contains protons and neutrons. In radioactive atoms, the nucleus is unstable and spontaneously emits radiation to reach a more stable configuration. This process is called radioactive decay.
α
Alpha (α) Decay
Emits a helium-4 nucleus (42He). Mass number −4, atomic number −2. Least penetrating — stopped by a sheet of paper.
β
Beta (β) Decay
Emits an electron from the nucleus (a neutron becomes a proton). Atomic number +1. Stopped by a few mm of aluminium.
γ
Gamma (γ) Radiation
High-energy electromagnetic radiation emitted after α or β decay. No change in mass or atomic number. Needs thick lead or concrete to stop.
Nuclear Equations
Nuclear equations show the transformation of one element into another (transmutation). Two conservation laws apply: the total mass number (top number) and the total atomic number (bottom number) must each be equal on both sides.
Alpha decay of Uranium-238:
23892U → 23490Th + 42He
Mass: 238 = 234 + 4 ✓ Atomic number: 92 = 90 + 2 ✓
Beta decay of Carbon-14 (used in carbon dating):
146C → 147N + 0−1e
Mass: 14 = 14 + 0 ✓ Atomic number: 6 = 7 + (−1) ✓
Half-Life
The half-life of a radioactive isotope is the time taken for half the radioactive nuclei in a sample to decay. Each half-life halves the remaining amount of the parent isotope. It is constant for any given isotope — independent of temperature, pressure, or chemical state.
Half-life decay table (starting with 80 g of isotope X, half-life = 10 days)
| Time (days) | Half-lives elapsed | Amount remaining |
|---|---|---|
| 0 | 0 | 80 g |
| 10 | 1 | 40 g |
| 20 | 2 | 20 g |
| 30 | 3 | 10 g |
| 40 | 4 | 5 g |
Applications of half-life: Carbon-14 dating (half-life ~5,730 years) is used to date organic material up to ~50,000 years old. Medical imaging uses short-lived isotopes (e.g., technetium-99m, half-life 6 hours) to minimise patient radiation exposure.
Nuclear Fission and Fusion
Nuclear Fission
A heavy nucleus splits into two smaller nuclei, releasing neutrons and enormous energy. A chain reaction occurs when released neutrons trigger further fissions.
235U + n → 141Ba + 92Kr + 3n + energy
Used in: nuclear power stations (controlled chain reaction) and nuclear weapons (uncontrolled).
Nuclear Fusion
Two light nuclei combine to form a heavier nucleus, releasing even more energy per unit mass than fission. Requires extremely high temperatures (~107 °C).
2H + 3H → 4He + n + energy
Used in: the Sun and stars (natural fusion). Experimental fusion reactors (e.g., ITER) aim to harness it for clean energy.
E = mc²: Einstein's famous equation explains why nuclear reactions release so much energy. Even tiny amounts of mass (m) converted to energy (E) produce huge results because c (the speed of light, 3 × 108 m/s) is squared.
Key Vocabulary
| Term | Definition |
|---|---|
| Radioactive decay | The spontaneous emission of radiation from an unstable nucleus as it transforms into a more stable configuration. |
| Half-life | The time for half of the radioactive nuclei in a sample to decay. It is constant for any given isotope. |
| Fission | The splitting of a heavy nucleus into two lighter nuclei, releasing large amounts of energy and neutrons. |
| Fusion | The joining of two light nuclei to form a heavier nucleus, releasing even greater amounts of energy per unit mass. |
Worked Examples
Complete: 22688Ra → ? + 42He (alpha decay of radium)
Step 1: Conservation of mass number: 226 = ? + 4 → ? = 222.
Step 2: Conservation of atomic number: 88 = ? + 2 → ? = 86.
Step 3: Element with atomic number 86 is Radon (Rn).
Answer: 22688Ra → 22286Rn + 42He
A sample of iodine-131 has a half-life of 8 days. If you start with 100 g, how much remains after 24 days?
Step 1: Number of half-lives = 24 ÷ 8 = 3 half-lives.
Step 2: After 1 half-life: 100 ÷ 2 = 50 g.
Step 3: After 2 half-lives: 50 ÷ 2 = 25 g.
Step 4: After 3 half-lives: 25 ÷ 2 = 12.5 g.
Answer: 12.5 g of iodine-131 remains after 24 days.
Why is nuclear fusion considered a more attractive energy source than fission, even though it is harder to achieve?
Fuel: Fusion uses hydrogen isotopes (deuterium and tritium), which are abundant. Deuterium can be extracted from seawater.
Waste: Fusion produces helium (non-radioactive) and neutrons, generating far less long-lived radioactive waste than fission.
Energy output: Fusion releases approximately 4 times more energy per kilogram of fuel than fission.
Safety: A fusion reactor cannot undergo a runaway chain reaction, making it inherently safer.
Challenge: Achieving the temperatures needed (>108 °C) and containing the plasma is an unsolved engineering problem.
Knowledge Check
Select the correct answer for each question.
Question 1
Which type of radiation is most penetrating?
Question 2
A radioactive isotope has a half-life of 20 years. Starting with 160 g, how much remains after 60 years?
Question 3
In beta decay, what happens to the atomic number of the decaying nucleus?
Question 4
Which process powers the Sun?
Question 5
What is conserved in every nuclear equation?
Key Concepts Summary
- •Three types of nuclear radiation: alpha (least penetrating), beta, and gamma (most penetrating).
- •Nuclear equations conserve both the mass number and the atomic number.
- •Half-life is the time for half the radioactive atoms in a sample to decay; it is constant and unaffected by environment.
- •Fission splits a heavy nucleus (used in nuclear reactors); fusion joins light nuclei (powers the Sun).
- •E = mc² explains the enormous energy released in nuclear reactions from tiny amounts of mass.