15.1
Types of Radioactive Emission
RadioactivityThe spontaneous emission of particles or electromagnetic radiation from unstable atomic nuclei. Radioactive decay is a first-order process: it is random, unaffected by temperature, pressure, or chemical state, and governed only by the decay constant λ.
| Radiation | Symbol / Nature | Charge | Mass (u) | Range in air | Stopped by | Ionising power |
|---|---|---|---|---|---|---|
| Alpha (α) | 42He nucleus (2p + 2n) | +2 | 4 | ~5 cm | Paper or skin | Very high |
| Beta (β−) | Electron (e−) from nucleus (neutron → proton) | −1 | ~0 | ~1 m | Few mm Al | Moderate |
| Beta (β+) | Positron (e+) from nucleus (proton → neutron) | +1 | ~0 | ~1 m | Few mm Al (then γ from annihilation) | Moderate |
| Gamma (γ) | High-energy electromagnetic radiation | 0 | 0 | Unlimited | Several cm Pb or thick concrete | Low |
| Neutron (n) | Neutral particle | 0 | 1 | Depends on energy | Water/polyethylene (hydrogenous) | Indirect (activates nuclei) |
Deflection in Fields
In electric field: α deflected toward negative plate (+ charge)
β¯ deflected toward positive plate (− charge)
γ undeflected (no charge)
In magnetic field (B out of page, beam into page):
α: deflected (e.g. downward if positive, using F=qv×B)
β¯: deflected opposite direction (lighter → larger arc)
γ: undeflected
15.2
Nuclear Equations
Nuclear Equation RulesConservation laws: (1) Mass number A (nucleons) is conserved. (2) Atomic number Z (protons) is conserved. (3) Charge is conserved. The notation: AZX. Check: sum of top numbers on left = sum on right; sum of bottom numbers on left = sum on right.
Types of Decay — Examples
Alpha decay (α): A decreases by 4; Z decreases by 2
22688Ra → 22286Rn + 42He
23892U → 23490Th + 42He
Beta-minus decay (β¯): n → p + e¯ + ν̄; A unchanged; Z increases by 1
146C → 147N + 0-1e
9038Sr → 9039Y + 0-1e
Beta-plus decay (β+): p → n + e+ + ν; A unchanged; Z decreases by 1
2211Na → 2210Ne + 0+1e
Gamma emission (γ): follows α or β decay; A, Z unchanged
Nucleus in excited state → ground state + γ photon
Electron capture: p + e¯ → n + ν; A unchanged; Z decreases by 1
4019K + 0-1e → 4018Ar + ν
15.3
Radioactive Decay and Half-Life
Radioactive Decay LawN = N₀e−λt and A = A₀e−λt, where N = number of atoms remaining, N₀ = initial atoms, λ = decay constant (s−1), A = activity (Bq). The half-life t½ = ln2/λ = 0.693/λ. Activity A = λN.
Decay Calculations
Half-life formula: N/N₀ = (1/2)^(t/t½) = e^(−λt)
Example: I-131 has t½ = 8.0 days; initial activity = 400 MBq
After 24 days: number of half-lives = 24/8 = 3
Activity = 400 × (1/2)³ = 400/8 = 50 MBq
Finding t½ from decay constant:
λ = 0.693/t½ ↔ t½ = 0.693/λ
Example: λ = 1.21×10⁻⁴ yr⁻¹ (for C-14)
t½ = 0.693/(1.21×10⁻⁴) = 5730 yr
Time to reach a given fraction:
t = −ln(N/N₀)/λ = t½ × log(N₀/N)/log2
Radiocarbon Dating
Living organisms maintain constant 14C/12C ratio (same as atmosphere) by continuous exchange. After death, 14C decays (t½ = 5730 yr) without replenishment. Measuring the remaining activity allows age calculation:
t = (t½/ln2) × ln(A₀/A)
Example: Wooden artefact has activity = 6.0 dpm/g; living wood = 13.6 dpm/g
t = (5730/0.693) × ln(13.6/6.0) = 8266 × 0.820 = 6780 yr
Range: ~300 – 60,000 years (beyond this, too little C-14 remains)
15.4
Decay Series
Decay Series (Chain)A sequence of radioactive decays from a heavy nucleus until a stable nucleus is reached. Each decay produces a new nuclide (called a daughter nuclide) which may itself be radioactive.
Uranium-238 Decay Series
238U → 234Th → 234Pa → 234U → 230Th → 226Ra → 222Rn → ...
... → 210Pb → 210Bi → 210Po → 206Pb (stable)
14 steps total (8 α decays + 6 β¯ decays)
Net change: A decreases by 32 (8×4), Z decreases by 10 (8×2−6×1)
Uranium-235 series: ends at Pb-207
Thorium-232 series: ends at Pb-208
Secular Equilibrium
If parent half-life ≫ daughter half-life, the daughter reaches secular equilibrium: its activity equals the parent's activity. Rate of formation of daughter = rate of decay. This is important in understanding radioactive waste and uranium ore chemistry.
15.5
Nuclear Fission and Fusion
Nuclear Binding EnergyE = mc² (Einstein's mass-energy equivalence). The binding energy per nucleon is the energy required to separate the nucleus into individual nucleons. Maximum stability occurs near Fe-56. Fission of heavy nuclei and fusion of light nuclei both release energy because products are more stable (higher binding energy/nucleon) than reactants.
| Nuclear Fission | Nuclear Fusion | |
|---|---|---|
| Definition | Heavy nucleus splits into two medium-sized nuclei + neutrons | Two light nuclei combine to form a heavier nucleus |
| Example | 235U + n → 141Ba + 92Kr + 3n + energy | 2H + 3H → 4He + n + 17.6 MeV |
| Conditions | Neutron bombardment; critical mass required | Extremely high T and P (>107 K, as in stars) |
| Energy per kg | ~8×1013 J/kg (uranium) | ~3.4×1014 J/kg (D-T) |
| Chain reaction | Yes (each fission releases 2–3 neutrons) | No self-sustaining chain (plasma conditions needed) |
| Waste | Radioactive fission products (long-lived) | Mainly He-4 (non-radioactive) + some tritium |
| Applications | Nuclear power plants, atomic bombs | Stars, H-bombs; future fusion reactors (ITER) |
Mass Defect and Energy Release
Mass defect: Δm = mass of reactants − mass of products
Energy released: E = Δm × c² (c = 3.0×10⁸ m/s)
Example: fusion of D + T:
Reactant masses: ²H = 2.01410 u; ³H = 3.01605 u; sum = 5.03015 u
Product masses: ⁴He = 4.00260 u; n = 1.00867 u; sum = 5.01127 u
Δm = 5.03015 − 5.01127 = 0.01888 u
E = 0.01888 × 931.5 MeV/u = 17.6 MeV per fusion event
(1 u = 931.5 MeV/c²)
15.6
Applications of Radioisotopes
| Application | Radioisotope | Radiation used | Principle |
|---|---|---|---|
| Radiocarbon dating | 14C (t½=5730 yr) | β | Decay of C-14 after death of organism |
| Geological dating | 238U (t½=4.5×109 yr), 40K | α, β | Parent/daughter ratio in rocks |
| Medical diagnosis (PET scan) | 18F, 11C (short t½) | β+ (annihilation γ) | Positron-emitting tracer; γ detected outside body |
| Medical diagnosis (SPECT) | 99mTc (t½=6 h) | γ only | Technetium-99m: gamma camera images organs |
| Medical therapy (cancer) | 131I, 60Co, 90Y | β, γ | Targeted delivery or external beam to destroy tumour cells |
| Food irradiation | 60Co, 137Cs | γ | Kill bacteria/mould in food without heat |
| Industrial radiography | 192Ir, 60Co | γ | Detect cracks in metal welds (like X-ray for pipes) |
| Thickness gauging | 85Kr, 90Sr | β | Absorption of β proportional to thickness |
| Smoke detectors | 241Am | α | α ionises air in chamber; smoke reduces current |
| Nuclear power | 235U, 239Pu | Fission neutrons | Controlled chain reaction heats water to drive turbines |
15.7
Health Hazards and Safety
Biological EffectsIonising radiation damages living tissue by ionising molecules (especially DNA and water). Direct damage: breaks chemical bonds. Indirect damage: ionised water produces free radicals (HO•) which attack DNA. Effects: cell death (at high doses = radiation sickness), DNA mutation (cancer risk), heritable genetic damage.
| Radiation | Biological hazard | Context |
|---|---|---|
| α | Most dangerous if inhaled or ingested (very high LET inside body); not hazardous externally (stopped by skin) | Radon gas (lung cancer), Po-210 poisoning |
| β | Penetrates skin; can cause burns and internal damage if ingested. Less ionising than α per unit path. | Sr-90 concentrated in bones (replaces Ca); I-131 in thyroid |
| γ | Penetrates body; whole-body exposure; lower ionisation density per path but long range means many cells affected | X-ray/CT dose; Chernobyl, Fukushima exposure |
Safety Measures
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TDS: Time, Distance, Shielding
Time: minimise exposure time; limit dose
Distance: intensity falls as 1/r² (inverse square law)
Shielding: paper/clothing for α; Al for β; Pb/concrete for γ
Dose units:
Gray (Gy) = 1 J/kg absorbed dose
Sievert (Sv) = Gray × Quality factor (QF)
QF: α = 20; β = 1; γ = 1; neutrons = 5–20
Annual background dose (UK avg): ~2.7 mSv/yr
Sources: radon (50%), medical (14%), cosmic rays (12%), food (12%)
Radioactive waste management:
Low-level: gloves, clothing → compaction, near-surface burial
Intermediate: → grouting in steel drums, underground storage
High-level (spent fuel): vitrification in borosilicate glass → deep geological disposal
✏️
Exercises
- Write balanced nuclear equations for: (a) alpha decay of 22286Rn; (b) beta-minus decay of 146C; (c) beta-plus decay of 2211Na; (d) identify the element X in: 23490Th → X + 0−1e.(a) 22286Rn → 21884Po + 42He. Check: 222=218+4 ✓; 86=84+2 ✓. (b) 146C → 147N + 0−1e. Check: 14=14+0 ✓; 6=7+(−1) ✓. (c) 2211Na → 2210Ne + 0+1e. Check: 22=22+0 ✓; 11=10+1 ✓. (d) X: A = 234, Z = 90−(−1) = 91 → Protactinium-234: 23491Pa. Equation: 23490Th → 23491Pa + 0−1e.
- Radon-222 has a half-life of 3.82 days. (a) Calculate the decay constant λ. (b) A sample contains 5.00 × 109 atoms at t=0. How many atoms remain after 2 weeks? (c) Calculate the activity at t=0 in Bq.(a) λ = ln2/t½ = 0.693/(3.82 days × 86400 s/day) = 0.693/330048 = 2.10×10−6 s−1. (b) t = 14 days; half-lives = 14/3.82 = 3.664. N = 5.00×109 × (1/2)3.664 = 5.00×109 × 0.0784 = 3.92×108 atoms. (c) A = λN = 2.10×10−6 × 5.00×109 = 10,500 Bq = 10.5 kBq.
- Compare alpha, beta, and gamma radiation in terms of: (a) nature and charge; (b) penetrating power; (c) ionising power; (d) biological hazard when source is external vs internal.(a) α: helium-4 nucleus, charge +2. β−: electron from nucleus, charge −1. γ: EM radiation, no charge. (b) Penetrating: α << β < γ. α stopped by paper; β by few mm Al; γ needs cm of Pb. (c) Ionising: α >> β > γ. α causes most ionisation per mm of path (dense ion trail). (d) External: γ most dangerous (penetrates body); α harmless (stopped by skin); β can cause skin burns. Internal (inhaled/ingested): α most dangerous (all energy deposited in local tissue, very high LET; e.g. Rn gas, Po-210). β dangerous (bone: Sr-90; thyroid: I-131). γ less so internally (energy escapes body).
- Describe how radiocarbon dating works. Include: the origin of C-14, the assumption made, the calculation method, and the limitation of the technique.Origin: Cosmic ray neutrons bombard N-14 in atmosphere: 14N + n → 14C + 1H. C-14 oxidises to 14CO2, absorbed by plants, enters food chain. Living organisms maintain same 14C/12C ratio as atmosphere (steady state). Assumption: atmospheric 14C/12C ratio has been constant over time (calibrated with tree rings, corals). After death: 14C decays (t½=5730 yr), no replenishment. Measure remaining activity A; known initial activity A₀: t = (t½/ln2)ln(A₀/A). Limitation: useful range ~300–60,000 yr (beyond: too little C-14); assumes constant atmospheric ratio (corrected by calibration curve); contamination from modern carbon must be avoided; cannot date inorganic material.
- A nuclear reactor uses uranium-235 fission. (a) Write a balanced nuclear equation for a fission reaction producing Ba-141, Kr-92, and neutrons. (b) Explain how a controlled chain reaction is maintained. (c) State one advantage and one disadvantage of nuclear power compared to fossil fuels.(a) 23592U + 10n → 14156Ba + 9236Kr + 310n. Check: 235+1=141+92+3 → 236=236 ✓; 92+0=56+36+0 → 92=92 ✓. (b) Each fission releases 2–3 neutrons. Controlled chain reaction: control rods (boron or hafnium) absorb excess neutrons to keep exactly 1 neutron per fission triggering next fission (criticality factor k=1). Moderator (water or graphite) slows neutrons to thermal energies for efficient capture by U-235. Emergency shut-down: insert all control rods (SCRAM). (c) Advantage: very low CO2 emissions during operation (climate benefit); enormous energy density (~106× more than coal per kg). Disadvantage: radioactive waste highly toxic with long half-lives (requires thousands of years of safe storage); risk of meltdown accidents (Chernobyl, Fukushima).
- Explain why α radiation is the most dangerous type when a radioactive source is ingested, even though it is the least penetrating externally.External hazard is limited by penetrating power. α stopped by skin → no entry to vital organs. Internal: once an α emitter is ingested or inhaled, it is inside the body and very close to vital cells. α particles have very high Linear Energy Transfer (LET = energy deposited per unit length of tissue). All ionising energy is deposited in a very short range (~40 μm in tissue) → very high local dose → severe cell damage and DNA double-strand breaks. γ passes through the body — much of its energy exits without being absorbed. Example: Polonium-210 (Po-210, α emitter) used to poison Alexander Litvinenko: small mass caused lethal dose; Ra-226 in luminous paint caused osteosarcoma in dial painters. Radon gas (Rn-222, α emitter) inhaled in mines is the second leading cause of lung cancer after smoking.
🧠
Quiz
Unit 15: Radioactivity
25 QsQ1
Which type of radiation is deflected toward the negative plate in an electric field?
Alpha (α) has charge +2 → attracted to negative plate. Beta-minus has charge −1 → attracted to positive plate. Gamma and neutrons are undeflected (no charge).
Q2
In alpha decay, what happens to the mass number and atomic number?
Alpha particle = 42He. A decreases by 4; Z decreases by 2. The daughter element is 2 places left in the periodic table. Example: 226Ra → 222Rn + α.
Q3
Which of these correctly represents beta-minus decay?
146C → 147N + 0−1e. β−: A unchanged, Z increases by 1 (neutron converts to proton). Check: 14=14+0 ✓; 6=7+(−1) ✓. This is radiocarbon decay used in radiocarbon dating.
Q4
Gamma radiation is emitted when:
γ emission = transition of excited nucleus to ground state. No change in mass number or atomic number. Often accompanies α or β decay. Gamma photons are electromagnetic radiation (very short wavelength, very high energy).
Q5
A radioactive isotope has a half-life of 20 years. After 80 years, the fraction remaining is:
Number of half-lives = 80/20 = 4. Fraction = (1/2)4 = 1/16. So 1/16 of the original remains (6.25%). 15/16 has decayed.
Q6
The decay constant λ is related to half-life by:
λ = ln2/t½ = 0.693/t½. This comes from the first-order decay law: N = N₀e−λt. At t = t½: N₀/2 = N₀e−λt½ → 1/2 = e−λt½ → ln2 = λt½. Units of λ: s−1, min−1, yr−1 etc.
Q7
Radioactive decay is a first-order process. This means:
Activity A = λN. As N decreases (atoms decay), A also decreases. The decay is independent of temperature, pressure, chemical environment — purely nuclear phenomenon. This is why half-life can be used as an absolute clock.
Q8
Which radioisotope is commonly used in smoke detectors?
Am-241 emits α particles which ionise air in a chamber, creating a small current. Smoke particles absorb α → current drops → alarm triggered. α source is safe (stopped by detector housing). Amount is tiny (~1 μg).
Q9
The main difference between nuclear fission and nuclear fusion is:
Both release energy due to the binding energy per nucleon curve (peaks at Fe-56). Fission: heavy nucleus (e.g. U-235) → medium nuclei (higher BE/nucleon). Fusion: light nuclei (D, T) → heavier nucleus (He-4, much higher BE/nucleon). Fusion releases more energy/kg but requires extreme conditions.
Q10
Carbon-14 dating is useful for:
Organic materials up to ~60,000 yr. Beyond this: too little C-14 remains to measure accurately. For older rocks, long-lived isotopes (U-238 t½=4.5 Gyr; K-40 t½=1.25 Gyr) are used. C-14 dating requires the material to have been living (incorporated C-14 during life).
Q11
Which radiation type has the highest ionising power per unit path length?
Alpha has the highest LET (Linear Energy Transfer). The doubly-charged, massive α particle interacts strongly with electrons in tissue. In just ~40 μm of tissue, it deposits all its kinetic energy. This makes it extremely damaging to tissue it can reach (internal sources).
Q12
Technetium-99m (99mTc) is ideal for medical imaging because:
Tc-99m: pure γ emitter (no α or β = no ionising particles deposited in tissue); 140 keV γ optimal for detection; t½=6h (decays rapidly after imaging, minimising dose); "m" = metastable (excited nuclear state). Over 40 million procedures/year worldwide.
Q13
The uranium-238 decay series ends at:
Lead-206 (206Pb) is the stable end product of the U-238 decay series. 14 steps (8 α + 6 β− decays). From 238U: A decreases by 32 (8×4), Z decreases by 10 (8×2 − 6×1 = 10): 92−10=82=Pb; 238−32=206. ✓
Q14
Why does increasing temperature NOT affect radioactive decay rate?
Nuclear process: decay involves nuclear forces, not chemical bonds. Temperature affects electron energies and chemical bond energies (eV scale). Nuclear binding energies are millions of times larger (MeV scale). Thermal energies (~0.025 eV at 300 K) are completely negligible on nuclear energy scales. Decay constant λ is a pure nuclear property.
Q15
In PET (Positron Emission Tomography), the detected radiation is:
F-18 emits β+. Positron travels ~1mm then meets an electron: annihilation → two 511 keV γ photons emitted in opposite directions (180° apart). Detected simultaneously by ring of detectors → precise localisation. F-18 attached to glucose (FDG) concentrates in metabolically active tissues (tumours, brain).
Q16
The activity (A) of a radioactive source is measured in:
Becquerel (Bq) = 1 decay per second. Old unit: Curie (Ci) = 3.7×1010 Bq. Gray = absorbed dose (energy/mass). Sievert = effective dose (Gray × quality factor). eV = energy unit. Activity = λN.
Q17
Which statement about background radiation is correct?
Most background radiation is natural. In the UK: radon (~50%), food/drink (~12%), cosmic rays (~12%), gamma from ground/buildings (~15%), medical imaging (~14%), nuclear industry (<1%). Radon from uranium-containing rocks (granite) is the biggest single source and a significant lung cancer risk in affected areas.
Q18
Nuclear fission of U-235 produces a chain reaction because:
Chain reaction: each U-235 fission releases 2–3 neutrons. If at least 1 neutron per fission triggers another fission (criticality), chain is self-sustaining. Control rods absorb excess neutrons (prevent runaway). Critical mass ensures enough U-235 for neutrons to be captured (not escape) before hitting another nucleus.
Q19
The biological hazard of radiation is measured in Sieverts (Sv) rather than Grays (Gy) because:
Quality factor (QF): equal absorbed doses (Gray) produce different biological damage depending on radiation type. Sv = Gy × QF. QF: γ=1, β=1, α=20, fast neutrons=5–20. 1 Gy of α causes 20× more biological damage than 1 Gy of γ. The Sv gives the biologically equivalent dose.
Q20
Strontium-90 is particularly hazardous as a fission product because:
Sr-90 chemistry mimics calcium (same group 2); absorbed into bone tissue. t½=29 yr → long-term irradiation of bone marrow (bone marrow produces blood cells → leukaemia risk). Emits β− (and daughter Y-90 emits energetic β). Major concern in nuclear fallout from weapons testing and accidents.
Q21
Iodine-131 (t½ = 8 days) is used in thyroid cancer treatment because:
Thyroid takes up iodine to make thyroid hormones. Giving radioactive I-131 orally → concentrates in thyroid → β radiation (range ~1mm) destroys thyroid cells locally with minimal harm to surrounding tissue. t½=8 days: short enough to limit exposure but long enough for treatment effect. Also used to diagnose thyroid function (imaging) with smaller doses.
Q22
A decay series transforms 238U to 206Pb via 8 alpha and 6 beta-minus decays. Verify these numbers using conservation laws.
Conservation: A: 8α each remove 4; 8×4=32; 238−32=206 ✓. Z: 8α each remove 2 protons (=16 removed); 6β− each add 1 proton (=6 added); net ΔZ = 16−6=10; 92−10=82 (Pb) ✓. This is a good check method for any decay series problem.
Q23
Food irradiation using gamma rays from Co-60:
γ irradiation kills pathogens (Salmonella, E. coli, Listeria) and inhibits sprouting in vegetables by ionising their DNA. It does NOT make food radioactive (no neutron bombardment; γ doesn't activate stable nuclei). Approved in 60+ countries. Used on spices, dried herbs, some fruits, and ground beef in many regions. The food is safe to eat immediately.
Q24
In a nuclear power station, the moderator's role is to:
Moderator (water, heavy water, graphite) slows neutrons from MeV (fast) to ~0.025 eV (thermal). U-235 has a much larger fission cross-section for thermal neutrons (more likely to be captured and fissioned). Without moderator, most fast neutrons escape or are captured by U-238 without fission. Control rods (absorb neutrons) are different from moderator (slow neutrons).
Q25
High-level nuclear waste is particularly challenging because:
Spent nuclear fuel contains fission products (Cs-137 t½=30 yr, Sr-90 t½=29 yr) and actinides (Pu-239 t½=24,100 yr, Am-241 t½=432 yr). The waste must be safely contained for 10 half-lives (~240,000 yr for Pu-239). Solution: vitrification (mix with borosilicate glass) then deep geological disposal (stable rock formations at 500–1000 m depth). Ongoing controversy about suitable sites.
Unit 15 Quiz — Radioactivity (25 Questions)
Select one answer eachQ1
Alpha (α) radiation consists of:
α particle = ⁴₂He nucleus. Highly ionising, low penetration (stopped by paper or a few cm of air).
Q2
Beta-minus (β⁻) decay involves:
β⁻: ¹₀n → ¹₁p + ⁰₋₁e + ν̄ₑ. Mass number unchanged, atomic number +1. More penetrating than α.
Q3
Gamma (γ) radiation is:
γ rays: very penetrating, no mass or charge. Often emitted after α or β decay when nucleus is still in excited state.
Q4
Half-life (t₁/₂) is defined as:
t₁/₂ = ln2/λ = 0.693/λ. Each half-life reduces amount to half. After n half-lives: N = N₀(½)ⁿ.
Q5
The decay constant λ is related to half-life by:
Activity A = λN. Larger λ = shorter t₁/₂ = more rapidly decaying. λ has units of s⁻¹ (or min⁻¹, yr⁻¹ etc.).
Q6
Radioactive decay is a first-order process meaning:
First-order: constant half-life, exponential decay, rate depends only on amount present. Independent of temperature.
Q7
Beta-plus (β⁺) decay produces:
β⁺: ¹₁p → ¹₀n + ⁰₊₁e + νₑ. Mass number unchanged, Z decreases by 1. Occurs in proton-rich nuclei.
Q8
Nuclear fission involves:
E.g. ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n + energy. Chain reaction possible. Basis of nuclear power and weapons.
Q9
Nuclear fusion involves:
E.g. ²H + ³H → ⁴He + n + 17.6 MeV. Fusion releases more energy per kg than fission. Powers the sun.
Q10
Mass defect in a nucleus refers to:
Δm = (mass of protons + neutrons) – nuclear mass. E = Δmc² = binding energy holding the nucleus together.
Q11
The most stable nuclei have:
Maximum binding energy/nucleon at A≈56 (Fe, Ni). Elements lighter or heavier than Fe can release energy by fusion or fission respectively.
Q12
Electron capture involves:
K-capture: ¹₁p + ⁰₋₁e → ¹₀n + νₑ. Competes with β⁺ decay. Followed by X-ray emission as electron from outer shell fills vacancy.
Q13
Radiocarbon dating is limited to approximately:
After ~8–10 half-lives (8 × 5730 = 45,840 yr), ¹⁴C falls below detection. ¹⁴C dating range ~500–50,000 years.
Q14
The becquerel (Bq) is the SI unit of radioactivity equal to:
1 Bq = 1 decay s⁻¹. Activity A = λN (Bq). Old unit: curie (1 Ci = 3.7×10¹⁰ Bq).
Q15
Background radiation comes from:
~85% background radiation is natural. Radon (from uranium decay in rocks) is the largest natural source in many countries.
Q16
Alpha particles are the most ionising but least penetrating because:
α particles travel only a few cm in air; stopped by paper or skin. But internally (ingested/inhaled) they are most dangerous.
Q17
Gamma radiation is most penetrating because:
No charge, no mass → rarely interacts. Used in radiotherapy (focused on tumours), industrial imaging, and sterilisation.
Q18
In nuclear equations, conservation requires:
Sum of A left = sum of A right; sum of Z left = sum of Z right. Charge conservation ensures Z balances.
Q19
²³⁸U undergoes α decay to give:
α decay: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. A: 238–4=234; Z: 92–2=90 (Thorium).
Q20
Nuclear medicine uses radioactive isotopes that emit:
γ-emitters (e.g. ⁹⁹ᵐTc) pass through tissue and are detected. β⁺ produces annihilation γ-rays for PET scanning.
Q21
Spent nuclear fuel is highly radioactive due to:
Fission creates ~200 different isotopes. Short-lived ones dominate initial activity; long-lived ones (Pu, Am) persist for millennia.
Q22
The biological effect of radiation depends on:
Equivalent dose (Sv) = absorbed dose (Gy) × radiation weighting factor. α factor = 20; β, γ = 1.
Q23
Strontium-90 (⁹⁰Sr) is a dangerous fallout product because:
⁹⁰Sr is chemically similar to Ca → concentrates in bones. Long t₁/₂ and β emission make it a long-term radiation hazard.
Q24
Nuclear chain reactions require a critical mass because:
Critical mass = minimum mass for self-sustaining chain reaction. Each fission must produce on average ≥1 neutron that causes another fission.
Q25
Iodine-131 is used in treating thyroid cancer because:
¹³¹I concentrates in the thyroid (which uses I to make hormones). β⁻ emission destroys cancer cells locally with minimal systemic damage.
📝
Unit Test — 50 marks
Section A
30 marksQ1 [8 marks]
Complete and balance the following nuclear equations, identifying the unknown nuclide X in each case:
(a) 23592U + 10n → X + 9036Kr + 310n [2]
(b) 21884Po → X + 42He [2]
(c) X → 23491Pa + 0−1e [2]
(d) 2713Al + 42He → X + 10n [2]
(a) A: 235+1=236=AX+90+3; AX=236−90−3=143. Z: 92+0=ZX+36+0; ZX=56=Ba. X = 14356Ba. (b) A: 218=AX+4; AX=214. Z: 84=ZX+2; ZX=82=Pb. X = 21482Pb. (c) A: AX=234+0=234. Z: ZX=91+(−1)=90=Th. X = 23490Th. (d) A: 27+4=AX+1; AX=30. Z: 13+2=ZX+0; ZX=15=P. X = 3015P. (This is actually how P-30 was first synthesised by Irène Curie and Frédéric Joliot in 1934.)
Q2 [7 marks]
Phosphorus-32 (32P) is a β− emitter used in cancer treatment with a half-life of 14.3 days. A hospital receives a vial containing 185 MBq (megabecquerels) of activity.
(a) Write the nuclear equation for the decay of P-32. [2]
(b) Calculate the decay constant in s−1. [2]
(c) Calculate the activity after 30 days. [2]
(d) After how many days will the activity fall below 5 MBq? [1]
(a) 3215P → 3216S + 0−1e (+ antineutrino). Check: 32=32; 15=16+(−1)=15 ✓. (b) t½=14.3 days=14.3×86400=1.235×106 s. λ=ln2/t½=0.693/(1.235×106)=5.61×10−7 s−1. (c) A=A₀e−λt=185×e−(0.693/14.3)×30=185×e−1.453=185×0.234=43.3 MBq. (Alternatively: 30/14.3=2.10 half-lives; 185×(1/2)2.10=185×0.234=43.3 MBq ✓). (d) 5=185×(1/2)n; (1/2)n=5/185=0.0270; n=log(0.0270)/log(0.5)=5.21 half-lives; t=5.21×14.3=74.5 days.
Q3 [7 marks]
Compare nuclear fission and nuclear fusion under the following headings: (a) definition and examples [2]; (b) energy released (which produces more per kilogram, and why) [2]; (c) challenges preventing widespread use of fusion for power generation [3].
(a) Fission: a heavy nucleus (e.g. U-235, Pu-239) absorbs a neutron and splits into two medium-mass fission fragments + neutrons + energy. Example: 235U + n → 141Ba + 92Kr + 3n. Fusion: two light nuclei combine to form a heavier, more stable nucleus + energy. Example: 2H + 3H → 4He + n + 17.6 MeV. (b) Fusion produces more energy per kilogram (~3.4×1014 J/kg for D-T vs ~8×1013 J/kg for U-235 fission). Reason: fusion of H isotopes to He has a much larger mass defect per nucleon than fission. Also, D-T fuel is nearly limitless (deuterium from seawater) whereas U-235 is rare. (c) Challenges: (i) Plasma confinement: D-T fusion requires T>108 K (to overcome Coulomb repulsion). At this temperature all matter is plasma — must be confined by magnetic fields (tokamak: ITER) or laser compression (inertial confinement). No material can contain plasma at this temperature directly. (ii) Energy break-even: no fusion reactor has yet produced more energy than consumed (Q>1 sustained). ITER aims to produce Q=10. (iii) Tritium supply: T (t½=12.3 yr) is rare; must be bred from Li in reactor blanket. (iv) Neutron activation: 14 MeV neutrons from D-T fusion activate reactor materials, producing radioactive waste (though much shorter-lived than fission waste).
Q4 [8 marks]
A wooden beam from an ancient building is found to have a C-14 activity of 3.1 disintegrations per minute per gram of carbon (dpm/g). Living wood gives 13.6 dpm/g. (a) Explain why C-14 activity of living organisms remains constant. [2] (b) Calculate the age of the wood. (t½ of C-14 = 5730 yr) [3] (c) State two assumptions made in radiocarbon dating and one limitation of the method. [3]
(a) Cosmic ray neutrons produce C-14 in the upper atmosphere (14N + n → 14C + H). C-14 oxidises to 14CO2, enters the carbon cycle. Living organisms constantly exchange carbon with the atmosphere (plants by photosynthesis, animals by eating), maintaining the same 14C/12C ratio as the atmosphere (steady state: production rate = decay rate). At death, exchange stops. (b) A/A₀ = 3.1/13.6 = 0.228. t = −(t½/ln2)×ln(A/A₀) = −(5730/0.693)×ln(0.228) = −8268×(−1.478) = 12,200 years (approximately 12,200 yr old). (c) Assumptions: (i) The 14C/12C ratio in the atmosphere has been constant over time (in practice, calibrated using tree rings and corals). (ii) The wood has not exchanged carbon since death (no contamination by modern or fossil carbon). (iii) The initial activity per gram was the same as modern living wood. Limitation: useful only for organic (carbon-containing) material that was once living; upper limit ~60,000 yr (insufficient C-14 to measure beyond); contamination by even small amounts of modern carbon can give falsely young dates; must use calibration curve to correct for atmospheric 14C variations.
Section B
20 marksQ5 [10 marks]
Critically discuss the use of radioisotopes in medicine. Include: (a) principles and examples of diagnostic imaging (PET and SPECT) [4]; (b) principles and examples of therapeutic applications [3]; (c) the risk-benefit analysis a physician must consider when prescribing radioactive treatments [3].
(a) PET (Positron Emission Tomography): β+-emitting tracer (F-18 fluorodeoxyglucose = FDG) concentrates in metabolically active tissue (tumours, active brain areas). F-18 emits positron; it annihilates with nearby electron → two 511 keV γ photons in exactly opposite directions. Detected simultaneously by ring detectors (coincidence detection) → precise 3D localisation without surgery. Used for: cancer staging, neurological diseases (Alzheimer's), cardiac function. SPECT (Single Photon Emission CT): γ-emitting tracer (Tc-99m, t½=6h). Gamma camera rotates around patient → 3D images. Tc-99m: only γ emission (no β deposited in patient); optimal 140 keV energy for detectors; attaches to many pharmaceuticals for organ targeting (bone scans, lung perfusion, cardiac blood flow, kidney function). [4]
(b) Therapeutic uses: (i) Radioiodine (I-131, βγ, t½=8 days): thyroid concentrates iodine → destroys malignant/overactive thyroid tissue. Effective for thyroid cancer and hyperthyroidism. (ii) Targeted therapy: Y-90 (pure β, t½=64h) attached to monoclonal antibodies or microspheres delivered to liver tumours (SIRT = selective internal radiation therapy). (iii) External beam: Co-60 γ beam or linear accelerator X-rays directed at tumour from multiple angles (minimise dose to healthy tissue; tumours often more radiosensitive than healthy tissue). (iv) Brachytherapy: radioactive seeds (Pd-103, I-125) implanted directly in prostate. [3]
(c) Risk-benefit: Risks: (i) Radiation dose (stochastic: small lifetime cancer risk; deterministic: high dose tissue damage). (ii) Short-term side effects (nausea, bone marrow suppression). (iii) Risk of radioactive contamination of others (isolation needed post-I-131 therapy). Benefits: (i) Accurate diagnosis avoiding invasive biopsy. (ii) Targeted cancer therapy with fewer systemic side effects than chemotherapy. (iii) For life-threatening conditions (cancer), high radiation dose is justified if alternative is death. Considerations: age (younger patients have more to lose from radiation risk; prefer avoiding CT scans in children); pregnancy (foetus extremely radiosensitive); renal function (affects tracer clearance). ALARA principle: As Low As Reasonably Achievable — use minimum dose for diagnostic or therapeutic purpose. [3]
(b) Therapeutic uses: (i) Radioiodine (I-131, βγ, t½=8 days): thyroid concentrates iodine → destroys malignant/overactive thyroid tissue. Effective for thyroid cancer and hyperthyroidism. (ii) Targeted therapy: Y-90 (pure β, t½=64h) attached to monoclonal antibodies or microspheres delivered to liver tumours (SIRT = selective internal radiation therapy). (iii) External beam: Co-60 γ beam or linear accelerator X-rays directed at tumour from multiple angles (minimise dose to healthy tissue; tumours often more radiosensitive than healthy tissue). (iv) Brachytherapy: radioactive seeds (Pd-103, I-125) implanted directly in prostate. [3]
(c) Risk-benefit: Risks: (i) Radiation dose (stochastic: small lifetime cancer risk; deterministic: high dose tissue damage). (ii) Short-term side effects (nausea, bone marrow suppression). (iii) Risk of radioactive contamination of others (isolation needed post-I-131 therapy). Benefits: (i) Accurate diagnosis avoiding invasive biopsy. (ii) Targeted cancer therapy with fewer systemic side effects than chemotherapy. (iii) For life-threatening conditions (cancer), high radiation dose is justified if alternative is death. Considerations: age (younger patients have more to lose from radiation risk; prefer avoiding CT scans in children); pregnancy (foetus extremely radiosensitive); renal function (affects tracer clearance). ALARA principle: As Low As Reasonably Achievable — use minimum dose for diagnostic or therapeutic purpose. [3]
Q6 [10 marks]
Evaluate the role of nuclear power in addressing climate change. Discuss: (a) the physics of energy production in a nuclear reactor [3]; (b) advantages of nuclear power over fossil fuels [3]; (c) concerns about nuclear power (safety, waste, proliferation) and how they are addressed [4].
(a) Physics: U-235 fission triggered by thermal neutrons: 235U + n → fission fragments + 2–3 neutrons + ~200 MeV + γ. Chain reaction controlled (k=1) by: (i) Control rods (B or Hf) absorb excess neutrons; (ii) Moderator (water or graphite) slows fast neutrons to thermal energies for efficient U-235 capture; (iii) Coolant (water, CO2, liquid Na) removes heat → produces steam → drives turbine → generates electricity. Fuel: enriched uranium (3–5% U-235; natural uranium is 0.7%). Energy density: 1 kg U-235 yields ~8×1013 J (equivalent to ~3000 tonnes of coal). [3]
(b) Advantages: (i) Near-zero CO2 during operation: lifecycle emissions ~12 g CO2/kWh (comparable to wind); coal ~820 g/kWh. Essential for decarbonisation of baseload electricity. (ii) Very high energy density: small fuel volume, small plant footprint per GWh. (iii) Reliable baseload (unlike solar/wind which are intermittent); operates 24/7 regardless of weather. (iv) Uranium supply is diverse (stable geopolitics) and can be supplemented by thorium (abundant) or reprocessed plutonium. (v) Employment, economic development in host regions. [3]
(c) Concerns and responses: Safety: Chernobyl (1986): graphite-moderated RBMK reactor, design flaws, operator error → 31 direct deaths, ~4000 cancer deaths estimated. Modern Western reactors (PWR, BWR) use water as moderator (negative temperature coefficient: reactor self-stabilises). Post-Fukushima: passive safety systems (gravity-fed cooling, no active pumps required). Generation IV designs (molten salt, pebble bed) have inherently safe geometry. Statistically, nuclear power has fewest deaths/TWh of any energy source. Waste: High-level waste contains long-lived actinides. Strategy: vitrification + deep geological disposal (Onkalo facility in Finland is world's first). Reprocessing (UK, France) reduces waste volume. Waste volume is small (all US nuclear waste fits in one football field area). Proliferation: enriched fuel or reprocessed Pu could be diverted for weapons. Addressed by: IAEA safeguards and inspections; fuel leasing (countries return spent fuel to supplier nation); generation IV designs without easily separable Pu. Cost: nuclear capital costs very high (EDF Hinkley Point C: £33 billion). Learning curves and standardised modular reactors (SMRs) may reduce costs. Overall: nuclear power is likely necessary for a reliable, low-carbon electricity system, alongside renewables. [4]
(b) Advantages: (i) Near-zero CO2 during operation: lifecycle emissions ~12 g CO2/kWh (comparable to wind); coal ~820 g/kWh. Essential for decarbonisation of baseload electricity. (ii) Very high energy density: small fuel volume, small plant footprint per GWh. (iii) Reliable baseload (unlike solar/wind which are intermittent); operates 24/7 regardless of weather. (iv) Uranium supply is diverse (stable geopolitics) and can be supplemented by thorium (abundant) or reprocessed plutonium. (v) Employment, economic development in host regions. [3]
(c) Concerns and responses: Safety: Chernobyl (1986): graphite-moderated RBMK reactor, design flaws, operator error → 31 direct deaths, ~4000 cancer deaths estimated. Modern Western reactors (PWR, BWR) use water as moderator (negative temperature coefficient: reactor self-stabilises). Post-Fukushima: passive safety systems (gravity-fed cooling, no active pumps required). Generation IV designs (molten salt, pebble bed) have inherently safe geometry. Statistically, nuclear power has fewest deaths/TWh of any energy source. Waste: High-level waste contains long-lived actinides. Strategy: vitrification + deep geological disposal (Onkalo facility in Finland is world's first). Reprocessing (UK, France) reduces waste volume. Waste volume is small (all US nuclear waste fits in one football field area). Proliferation: enriched fuel or reprocessed Pu could be diverted for weapons. Addressed by: IAEA safeguards and inspections; fuel leasing (countries return spent fuel to supplier nation); generation IV designs without easily separable Pu. Cost: nuclear capital costs very high (EDF Hinkley Point C: £33 billion). Learning curves and standardised modular reactors (SMRs) may reduce costs. Overall: nuclear power is likely necessary for a reliable, low-carbon electricity system, alongside renewables. [4]