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

TermDefinition
RadioactivitySpontaneous emission of particles/energy from unstable atomic nuclei
Alpha (α) particle2 protons + 2 neutrons (⁴He nucleus); high ionising, low penetration
Beta (β) particleHigh-speed electron emitted from nucleus; moderate ionising and penetration
Gamma (γ) rayHigh-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 fissionSplitting a heavy nucleus (e.g., U-235) into smaller nuclei, releasing large amounts of energy
Nuclear fusionCombining light nuclei (e.g., H-2 + H-3) into a heavier nucleus, releasing even more energy
Big BangCosmological model: the universe began ~13.8 billion years ago in an extremely hot, dense state
Red shiftStretching of light waves from distant galaxies — evidence that galaxies are moving away and universe is expanding
CMBCosmic Microwave Background radiation — remnant heat from the Big Bang, evidence for the model
Main sequence starA star fusing hydrogen in its core; stable phase (Sun is a main sequence star)
E = mc²Einstein'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

PropertyAlpha (α)Beta (β)Gamma (γ)
NatureParticle: 2p + 2n (⁴He nucleus)Particle: fast electronElectromagnetic radiation
Charge+2−10 (neutral)
MassHigh (4 u)Very low (~1/1836 u)0
PenetrationLow: stopped by paper or few cm airModerate: stopped by 3 mm aluminiumHigh: requires several cm of lead or thick concrete
Ionising powerVery high (most dangerous inside body)ModerateLow
Effect on nucleusMass −4, atomic number −2Atomic number +1, mass unchangedNo change in atomic number or mass

Balancing Nuclear Equations

Conservation Laws
Mass number (A) is conserved: sum of A on left = sum of A on right
Atomic number (Z) is conserved: sum of Z on left = sum of Z on right
Alpha decay example: ⎓⁶⁸Ra → ₂₆₆Rn + ₄₂He
Check: mass 226 = 222 + 4 ✓; atomic number 88 = 86 + 2 ✓
Beta decay example: ₁₆C → ₇¹₄N + ₀−₁e (beta particle)
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.

Ionisation and Danger: Inside the body, alpha particles are most dangerous despite low penetration — they deposit all their energy locally, causing severe cell damage. Outside the body, gamma rays are most dangerous because they penetrate deep tissue. This distinction is critical for explaining radiation safety.

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

Formula
N = N₀ × (½)ⁿ      A = A₀ × (½)ⁿ

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

  1. Calculate n = total time ÷ half-life
  2. Apply the formula: N = N₀ × (½)ⁿ
  3. Alternatively, halve the quantity n times in sequence
  4. Include units in your answer

Half-Life Step Table (for verification)

Number of half-lives (n)Fraction remaining% remaining
01/1100%
11/250%
21/425%
31/812.5%
41/166.25%
51/323.125%
101/1024≈0.1%
Example: A sample has initial activity 800 Bq. Half-life = 6 years. Find activity after 18 years.
n = 18 ÷ 6 = 3 half-lives
A = 800 × (½)³ = 800 × ⅛ = 100 Bq
Never reaches zero: Radioactive decay is exponential, not linear. The activity halves each half-life but never reaches exactly zero. After 10 half-lives, ≈0.1% remains. This is why nuclear waste is dangerous for thousands of years.

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

PropertyFissionFusion
ProcessSplitting heavy nucleus (e.g., U-235)Joining light nuclei (e.g., ²H + ³H)
Energy releasedVery large (~200 MeV per reaction)Larger per unit mass (~17.6 MeV but higher energy density)
Current useNuclear power plants, weaponsThe Sun and stars; experimental (ITER tokamak)
FuelUranium-235, Plutonium-239 (rare, non-renewable)Deuterium & Tritium (from seawater — abundant)
Radioactive wasteLong-lived radioactive products (thousands of years)Helium (inert) + neutrons; much less problematic waste
StatusCommercially used worldwideNot yet commercially viable; under development
Conditions requiredNeutron bombardment; chain reactionExtreme temperature and pressure (>100 million °C)
E = mc²
Energy (J) = mass (kg) × speed of light² (3×10⁸ m/s)²
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.

Critical Distinction: Fission = splitting heavy nuclei (nuclear reactors, atomic bombs). Fusion = joining light nuclei (powers stars, being developed for clean energy). Both involve E = mc². A common exam error is confusing which is which.

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

Small stars (like our Sun):
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

StageProcess
NebulaCloud of gas (mainly H and He) and dust in space
ProtostarGravity pulls gas together; core heats up
Main sequenceHydrogen fusion in core; gravitational collapse balanced by radiation pressure — stable phase (billions of years)
Red giant/supergiantHydrogen exhausted in core; helium fusion begins; outer layers expand
SupernovaCatastrophic explosion of massive star; elements heavier than iron formed and scattered
Black holeRemnant 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.

CALCULATEA radioactive sample has a half-life of 6 years. If the initial activity is 800 Bq, calculate the activity after 18 years.
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Full Solution
Number of half-lives: n = 18 ÷ 6 = 3 half-lives

A = A₀ × (½)ⁿ = 800 × (½)³ = 800 × ⅛ = 100 Bq

Step-by-step verification: 800 → 400 → 200 → 100 Bq ✓
CALCULATEA sample originally contains 1200 radioactive atoms. Half-life = 4 years. How many atoms remain after 12 years?
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Full Solution
n = 12 ÷ 4 = 3 half-lives
N = 1200 × (½)³ = 1200 × ⅛ = 150 atoms

Sequence: 1200 → 600 → 300 → 150 ✓
BALANCEComplete the nuclear equation for alpha decay of Uranium-238: ⎙₂²⁸U → ? + ₂⁴He
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Full Solution
Conservation of mass number: 238 = A + 4 → A = 234
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 ✓
EXPLAINExplain why alpha particles are most dangerous when a source is inside the body, but gamma rays are most dangerous outside the body.
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Full Solution
Alpha particles inside the body: Alpha particles have very short range (a few cm in air; stopped by paper) but extremely high ionising power. When an alpha source is ingested or inhaled (e.g., radon gas), all the energy is deposited in a tiny volume of nearby tissue, causing severe DNA damage and significantly increasing cancer risk.

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.
COMPARECompare fission and fusion as energy sources for electricity generation.
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Full Solution
Fission (current technology): Splits U-235 using neutrons; chain reaction releases ~200 MeV per reaction. Currently used in nuclear power plants worldwide. Produces long-lived radioactive waste (thousands of years). Risk of accidents (Chernobyl 1986, Fukushima 2011). Non-renewable uranium fuel. Low carbon emissions during operation.

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.
EVIDENCEDescribe the red shift evidence for the expanding universe and the Big Bang.
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Full Solution
When astronomers examine the light spectrum from distant galaxies, the spectral lines are shifted toward longer (redder) wavelengths — this is called red shift. This is analogous to the Doppler effect for sound: the wavelength of light from a source moving away from the observer is stretched.

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.
EVALUATEEvaluate the use of nuclear power stations as a response to climate change.
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Full Solution
Scientific case for: Nuclear fission produces virtually no CO₂ during operation (lifecycle emissions ~12 g CO₂/kWh vs 820 for coal). Provides reliable, high-density baseload power unaffected by weather, unlike solar and wind.

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.

IDENTIFYWhich type of radiation is stopped by a sheet of paper? What are its charge and mass?
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Model Answer
Alpha (α) radiation is stopped by paper (or a few cm of air). It has a charge of +2 and a mass of 4 u (2 protons + 2 neutrons).
CALCULATEA radioactive isotope has a half-life of 5 years and an initial activity of 3200 Bq. What is the activity after 20 years?
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Model Answer
n = 20 ÷ 5 = 4 half-lives
A = 3200 × (½)⁴ = 3200 × 1/16 = 200 Bq
Sequence: 3200 → 1600 → 800 → 400 → 200 ✓
DISTINGUISHWhat is the difference between fission and fusion? Give one application of each.
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Model Answer
Fission: Splitting a heavy nucleus (e.g., U-235) into smaller nuclei + energy. Application: nuclear power stations, nuclear weapons.
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).
EVIDENCEState two pieces of evidence that support the Big Bang theory.
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Model Answer
1. Red shift of distant galaxies: Light from all distant galaxies is shifted to longer wavelengths (red-shifted), indicating they are moving away. More distant galaxies recede faster (Hubble's Law), showing the universe is expanding. Running time backward implies everything originated from one point.

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.
DESCRIBEDescribe the life cycle of a star like our Sun from nebula to final state.
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Model Answer
1. Nebula: Vast cloud of hydrogen and helium gas collapses under gravity.
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).
APPLYExplain why the half-life of a medical radioisotope should be short but not too short.
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Model Answer
Should be short: To minimise the total radiation dose received by the patient. A short half-life means activity decreases quickly, reducing long-term radiation exposure and risk.

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.
CALCULATEA carbon-14 sample from an archaeological site has 25% of the carbon-14 activity of a modern sample. If the half-life of C-14 is 5,730 years, estimate the age of the sample.
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Model Answer
25% = 1/4 of original activity.
(½)ⁿ = 1/4 → n = 2 half-lives (since (1/2)² = 1/4)
Age = 2 × 5,730 = 11,460 years
EVALUATEA student claims nuclear fusion is the perfect solution to global energy needs. Evaluate this claim.
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Model Answer
Evidence for the claim: Fusion uses hydrogen isotopes from seawater (effectively unlimited fuel), produces very little radioactive waste (mainly helium and short-lived neutron activation), has no risk of catastrophic meltdown, and releases enormous amounts of energy with essentially zero CO₂ emissions.

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.

State the three types of nuclear radiation and their penetration.
Alpha: stopped by paper. Beta: stopped by 3 mm aluminium. Gamma: requires several cm of lead or thick concrete.
Tap to reveal
Define half-life.
The time for half the radioactive nuclei in a sample to decay. It is constant for each radioactive isotope.
Tap to reveal
Half-life formula for activity.
A = A₀ × (½)ⁿ where n = number of half-lives = total time ÷ half-life.
Tap to reveal
What is nuclear fission?
Splitting a heavy nucleus (e.g., U-235) into smaller nuclei and energy when struck by a neutron. Used in nuclear power stations.
Tap to reveal
What is nuclear fusion?
Combining light nuclei (e.g., deuterium + tritium) into a heavier nucleus, releasing large amounts of energy. Powers the Sun and stars.
Tap to reveal
State E = mc² and explain its significance in nuclear reactions.
Energy = mass × (speed of light)². In nuclear reactions, a tiny amount of mass is converted to an enormous amount of energy, explaining the power of nuclear reactions.
Tap to reveal
State two pieces of evidence for the Big Bang.
1. Red shift of distant galaxies (expanding universe). 2. Cosmic Microwave Background radiation (CMB) — remnant heat from the Big Bang, ~2.7 K, detected from all directions.
Tap to reveal
What does red shift of a galaxy indicate?
The galaxy is moving away from us. The light waves are stretched to longer (redder) wavelengths — a Doppler-like effect. More distant galaxies show greater red shift (Hubble's Law).
Tap to reveal
Describe the main sequence stage of a star.
A stable phase where hydrogen fusion in the core produces radiation pressure that balances gravitational collapse. This phase lasts billions of years.
Tap to reveal
What is the final state of a small star (like our Sun)?
White dwarf (after passing through main sequence, red giant, and planetary nebula stages). Eventually becomes a black dwarf (theoretical).
Tap to reveal
Why are alpha particles most dangerous inside the body?
Alpha particles have very high ionising power but low penetration. Inside the body, all their energy is deposited in nearby tissue, causing severe DNA damage.
Tap to reveal
What laws must be conserved when balancing nuclear equations?
Conservation of mass number (A) and conservation of atomic number (Z). Both must be equal on both sides of the equation.
Tap to reveal
What happens in a supernova?
A massive star explodes catastrophically at the end of its life, scattering elements heavier than iron into space. Leaves behind either a neutron star or black hole.
Tap to reveal
Why is nuclear waste a long-term problem?
Fission products include isotopes with half-lives of thousands of years (e.g., Cs-137: 30 years; Pu-239: 24,100 years). Radioactivity decreases exponentially but never reaches zero quickly.
Tap to reveal
What is the Cosmic Microwave Background (CMB)?
Uniform microwave radiation detectable from all directions in space. It is the cooled remnant heat radiation from the Big Bang (~13.8 billion years ago), now at ~2.7 K.
Tap to reveal

Practice Test — 20 Questions

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