Nuclear Physics and Astrophysics
This topic spans the very small (atomic nuclei) to the very large (the universe). Nuclear physics covers radioactivity, half-life, and nuclear reactions. Astrophysics explores the life cycle of stars, evidence for the Big Bang, and humanity's place in the cosmos. Both areas are heavily tested in eAssessment, with emphasis on calculation, data interpretation, and ethical evaluation of nuclear technology.
What You'll Learn
- Describe alpha, beta, and gamma radiation — properties, penetration, and ionisation
- Calculate the remaining activity or number of atoms after multiple half-lives
- Write and balance nuclear equations for decay and fission/fusion
- Explain nuclear fission and fusion; compare their energy outputs and applications
- Describe the life cycle of stars based on their mass
- Explain the evidence for the Big Bang theory (red shift, CMB)
- Evaluate the social and ethical implications of nuclear technology
eAssessment Focus
Criterion A: Define and distinguish radiation types; explain nuclear processes with correct terminology.
Criterion B: Interpret graphs of radioactive decay; evaluate hypotheses about nuclear energy.
Criterion C: Calculate activity after n half-lives; balance nuclear equations.
Criterion D: Evaluate uses of nuclear technology (power, medicine, weapons) from scientific, ethical, social, and environmental perspectives.
Key Vocabulary
| Term | Definition |
|---|---|
| Radioactivity | Spontaneous emission of particles/energy from unstable atomic nuclei |
| Alpha (α) particle | 2 protons + 2 neutrons (⁴He nucleus); high ionising, low penetration |
| Beta (β) particle | High-speed electron emitted from nucleus; moderate ionising and penetration |
| Gamma (γ) ray | High-energy electromagnetic radiation; low ionising, very high penetration |
| Half-life (t₂) | Time for half the radioactive nuclei in a sample to decay; constant for each isotope |
| Nuclear fission | Splitting a heavy nucleus (e.g., U-235) into smaller nuclei, releasing large amounts of energy |
| Nuclear fusion | Combining light nuclei (e.g., H-2 + H-3) into a heavier nucleus, releasing even more energy |
| Big Bang | Cosmological model: the universe began ~13.8 billion years ago in an extremely hot, dense state |
| Red shift | Stretching of light waves from distant galaxies — evidence that galaxies are moving away and universe is expanding |
| CMB | Cosmic Microwave Background radiation — remnant heat from the Big Bang, evidence for the model |
| Main sequence star | A star fusing hydrogen in its core; stable phase (Sun is a main sequence star) |
| E = mc² | Einstein's mass-energy equivalence: a tiny mass converts to enormous energy in nuclear reactions |
Radioactivity
Radioactive decay is the spontaneous transformation of an unstable nucleus. The three types of radiation have very different properties and applications.
Types of Radiation — Comparison
| Property | Alpha (α) | Beta (β) | Gamma (γ) |
|---|---|---|---|
| Nature | Particle: 2p + 2n (⁴He nucleus) | Particle: fast electron | Electromagnetic radiation |
| Charge | +2 | −1 | 0 (neutral) |
| Mass | High (4 u) | Very low (~1/1836 u) | 0 |
| Penetration | Low: stopped by paper or few cm air | Moderate: stopped by 3 mm aluminium | High: requires several cm of lead or thick concrete |
| Ionising power | Very high (most dangerous inside body) | Moderate | Low |
| Effect on nucleus | Mass −4, atomic number −2 | Atomic number +1, mass unchanged | No change in atomic number or mass |
Balancing Nuclear Equations
Atomic number (Z) is conserved: sum of Z on left = sum of Z on right
Check: mass 226 = 222 + 4 ✓; atomic number 88 = 86 + 2 ✓
Mass: 14 = 14 + 0 ✓; Atomic number: 6 = 7 + (−1) ✓
Medical and Industrial Applications
Medical Imaging
Gamma emitters (e.g., Tc-99m) used in PET scans. Gamma passes through body to be detected externally. Short half-life minimises radiation dose.
Cancer Treatment
Targeted radiotherapy uses beta or gamma radiation to kill cancer cells. Requires precise targeting to minimise damage to healthy tissue.
Radiocarbon Dating
Carbon-14 (half-life ~5,730 years) used to date organic materials. Ratio of C-14 to C-12 decreases after death at a known rate.
Smoke Detectors
Americium-241 (alpha emitter) ionises air in detector. Smoke particles disrupt ion flow, triggering the alarm.
Half-Life Calculations
The half-life is the time for half a radioactive sample to decay. It is constant and unique for each radioactive isotope. Half-life calculations are a guaranteed calculation question in the eAssessment.
The Half-Life Formula
Where: N = number of atoms remaining, N₀ = initial atoms
A = activity remaining, A₀ = initial activity
n = number of half-lives elapsed = total time / half-life
Step-by-Step Method
- Calculate n = total time ÷ half-life
- Apply the formula: N = N₀ × (½)ⁿ
- Alternatively, halve the quantity n times in sequence
- Include units in your answer
Half-Life Step Table (for verification)
| Number of half-lives (n) | Fraction remaining | % remaining |
|---|---|---|
| 0 | 1/1 | 100% |
| 1 | 1/2 | 50% |
| 2 | 1/4 | 25% |
| 3 | 1/8 | 12.5% |
| 4 | 1/16 | 6.25% |
| 5 | 1/32 | 3.125% |
| 10 | 1/1024 | ≈0.1% |
n = 18 ÷ 6 = 3 half-lives
A = 800 × (½)³ = 800 × ⅛ = 100 Bq
Nuclear Fission & Fusion
Nuclear reactions release millions of times more energy per atom than chemical reactions, explained by Einstein's E = mc². Fission and fusion are opposite processes with crucial differences.
Fission vs Fusion
| Property | Fission | Fusion |
|---|---|---|
| Process | Splitting heavy nucleus (e.g., U-235) | Joining light nuclei (e.g., ²H + ³H) |
| Energy released | Very large (~200 MeV per reaction) | Larger per unit mass (~17.6 MeV but higher energy density) |
| Current use | Nuclear power plants, weapons | The Sun and stars; experimental (ITER tokamak) |
| Fuel | Uranium-235, Plutonium-239 (rare, non-renewable) | Deuterium & Tritium (from seawater — abundant) |
| Radioactive waste | Long-lived radioactive products (thousands of years) | Helium (inert) + neutrons; much less problematic waste |
| Status | Commercially used worldwide | Not yet commercially viable; under development |
| Conditions required | Neutron bombardment; chain reaction | Extreme temperature and pressure (>100 million °C) |
Even a tiny mass converts to enormous energy. 1 gram of matter ≡ 9 × 10₁₃ J
Evaluating Nuclear Power
Arguments For
Low carbon emissions (lifecycle); high energy density; reliable baseload power; not weather-dependent like solar/wind.
Arguments Against
Long-lived radioactive waste; risk of catastrophic accidents (Chernobyl, Fukushima); uranium mining impacts; high construction costs.
Astrophysics
Astrophysics applies physics to understand the universe: the life cycle of stars, the evidence for the Big Bang, and the scale and structure of the cosmos.
Life Cycle of Stars
Nebula → Protostar → Main Sequence Star → Red Giant → Planetary Nebula → White Dwarf → (Black Dwarf eventually)
Large stars (massive stars):
Nebula → Protostar → Main Sequence Star → Red Supergiant → Supernova → Neutron Star or Black Hole
Key Stages Explained
| Stage | Process |
|---|---|
| Nebula | Cloud of gas (mainly H and He) and dust in space |
| Protostar | Gravity pulls gas together; core heats up |
| Main sequence | Hydrogen fusion in core; gravitational collapse balanced by radiation pressure — stable phase (billions of years) |
| Red giant/supergiant | Hydrogen exhausted in core; helium fusion begins; outer layers expand |
| Supernova | Catastrophic explosion of massive star; elements heavier than iron formed and scattered |
| Black hole | Remnant of most massive stars; gravity so strong not even light escapes |
Evidence for the Big Bang
Red Shift
Light from distant galaxies is shifted to longer (red) wavelengths, indicating they are moving away. More distant galaxies show greater red shift — universe is expanding uniformly (Hubble's Law).
Cosmic Microwave Background (CMB)
Uniform microwave radiation detectable from all directions in space. Predicted by Big Bang theory as the cooled remnant of the hot early universe. Discovered in 1965 by Penzias and Wilson.
Abundance of Light Elements
Big Bang nucleosynthesis predicts ~75% hydrogen and ~25% helium in the early universe. This ratio matches observations across the universe.
Age of the Universe
Using Hubble's constant from red shift measurements, the universe is estimated at ~13.8 billion years old — consistent with the age of the oldest stars.
Worked Examples
These examples cover the full range of question types in the eAssessment, from calculation to evaluation.
A = A₀ × (½)ⁿ = 800 × (½)³ = 800 × ⅛ = 100 Bq
Step-by-step verification: 800 → 400 → 200 → 100 Bq ✓
N = 1200 × (½)³ = 1200 × ⅛ = 150 atoms
Sequence: 1200 → 600 → 300 → 150 ✓
Conservation of atomic number: 92 = Z + 2 → Z = 90
Element with Z = 90 is Thorium (Th).
Complete equation: ⎙₂²⁸U → ₉₀²³⁴Th + ₂⁴He
Check: mass 238 = 234 + 4 ✓; atomic number 92 = 90 + 2 ✓
Gamma outside the body: Gamma rays have very low ionising power but extremely high penetration (require cm of lead to stop). Outside the body, gamma rays pass through skin, muscles, and organs, potentially causing ionisation damage deep in the body. Alpha particles emitted outside the body are stopped by the outer layer of dead skin cells and cause no internal damage.
Fusion (future technology): Joins deuterium and tritium (from seawater — abundant). Produces ~17.6 MeV per reaction but higher energy per unit mass. Produces helium (inert) and neutrons — far less problematic waste. No chain reaction — no risk of runaway meltdown. Requires extreme temperatures (>100 million °C) and confinement — not yet commercially viable (ITER project aims for demonstration by 2030s).
Conclusion: Fusion would be a superior energy source if achieved, but fission is the current reality.
Hubble's observation (1929): More distant galaxies show greater red shift — they are moving away faster. This implies the universe is expanding uniformly.
Connection to Big Bang: If the universe is expanding, then in the past all matter was closer together. Extrapolating backwards in time, everything converges to a single hot, dense point ~13.8 billion years ago — the Big Bang. Red shift is the primary observational evidence for this model.
Scientific concerns: Uranium mining and enrichment have environmental impacts. Spent fuel remains radioactive for thousands of years — no permanent geological storage solution yet operational. Small risk of catastrophic accidents (though modern reactor designs have passive safety systems).
Economic: Nuclear plants are very expensive and slow to build (often 10–20 years). However, once built, fuel costs are low and plants operate for 40–60 years.
Social/ethical: Public opposition (especially after Chernobyl and Fukushima); questions about intergenerational justice (leaving waste for future generations); proliferation risk (nuclear technology can be adapted for weapons).
Conclusion: Nuclear power is a low-carbon technology that could play a role in reducing emissions, but must be weighed against waste, safety, cost, and proliferation concerns. A diverse energy mix, including renewables, is likely the most sustainable path.
Practice Q&A
Attempt each question before revealing the answer. Show all working for calculation questions.
A = 3200 × (½)⁴ = 3200 × 1/16 = 200 Bq
Sequence: 3200 → 1600 → 800 → 400 → 200 ✓
Fusion: Combining light nuclei (e.g., ²H + ³H → ⁴He) to form a heavier nucleus + energy. Application: powers the Sun and all stars; being developed for clean energy generation (ITER).
2. Cosmic Microwave Background (CMB): A uniform background of microwave radiation detectable from all directions in space. This is the remnant heat from the Big Bang, now cooled to ~2.7 K, consistent with theoretical predictions.
2. Protostar: Core temperature rises as gas condenses; fusion has not yet begun.
3. Main sequence star: Hydrogen fusion begins; radiation pressure balances gravity — stable for ~10 billion years (the Sun is ~4.6 billion years old).
4. Red giant: Hydrogen core exhausted; helium fusion begins; outer layers expand and cool (red).
5. Planetary nebula: Outer layers expelled into space.
6. White dwarf: Dense core remains; no fusion; slowly cools.
7. (Eventually) Black dwarf: Theoretical final state after cooling completely (none yet exist).
Should not be too short: The radioisotope must remain active long enough for the medical procedure to be completed (e.g., scanning), for the substance to reach the target organ, and for detection equipment to record it. If the half-life is too short, the radioisotope decays before it can be useful.
Example: Technetium-99m has a half-life of ~6 hours — long enough for imaging scans to be completed but short enough to minimise patient radiation dose.
(½)ⁿ = 1/4 → n = 2 half-lives (since (1/2)² = 1/4)
Age = 2 × 5,730 = 11,460 years
Limitations of the claim: Fusion has not yet achieved "ignition" on a commercial scale — more energy is currently put in than extracted. Extreme conditions required (>100 million °C) make confinement extraordinarily difficult and expensive. ITER (the international test reactor) aims to demonstrate feasibility; commercial fusion power is decades away. Materials exposed to neutron radiation become radioactive over time (activation).
Conclusion: The claim exaggerates current technological readiness. Fusion shows enormous promise but cannot yet be called a "solution" — it remains an important research goal that may transform energy by the late 21st century.
Flashcard Review
Tap each card to reveal the answer. Try to answer from memory first.