Nuclear Decay and Radioactivity (AAMC 4E)
Nuclear Physics studies the nucleus, its composition, the radiation it emits, and the rules governing radioactive decay. The AAMC MCAT content outline emphasizes nuclide notation, half-life calculations, and medical/biological applications.
Composition of Atomic Nuclei
An atomic nucleus is composed of protons (positive charge, +1.6×10-19 C) and neutrons (uncharged), collectively called nucleons. A nuclide is written as AZX where:
- Z (atomic number)
- Number of protons; defines the chemical element.
- A (mass number)
- Total number of nucleons (protons + neutrons).
- N (neutron number)
- N = A − Z.
Isotopes: same Z, different A (e.g. 1H, 2H, 3H).
Isobars: same A, different Z (e.g. 14C, 14N).
Isotones: same N, different Z.
Mass defect and binding energy
The mass of a nucleus is always less than the sum of the rest-masses of its constituent nucleons. The difference is the mass defect Δm, and is converted to binding energy:
E = Δm·c²
The binding energy per nucleon is highest at iron (56Fe, ≈ 8.8 MeV/nucleon) which is why iron is the most stable nucleus. Lighter nuclei release energy by fusion; heavier nuclei release energy by fission.
Spontaneous and Random Nuclear Decay
Radioactive decay is the spontaneous emission of particles or radiation from an unstable nucleus. Two key features:
- Spontaneous: not affected by external conditions (temperature, pressure, chemical state).
- Random: we cannot predict when any individual nucleus will decay; we can only state a probability.
Types of decay
| Property | α decay | β− decay | β+ decay | γ decay |
|---|---|---|---|---|
| Particle emitted | 42He nucleus (2p + 2n) | Electron (e−) + antineutrino | Positron (e+) + neutrino | High-energy photon |
| Charge | +2 | −1 | +1 | 0 |
| Mass | 4 u | ~1/1836 u | ~1/1836 u | 0 |
| Effect on A (mass no.) | A − 4 | Unchanged | Unchanged | Unchanged |
| Effect on Z (atomic no.) | Z − 2 | Z + 1 (n → p) | Z − 1 (p → n) | Unchanged |
| Speed | ~0.05c | up to ~0.99c | up to ~0.99c | c (speed of light) |
| Ionising power | Highest | Medium | Medium | Lowest |
| Penetrating power | Lowest, stopped by paper / few cm air | Medium, stopped by ~3 mm Al | Medium, like β−, then annihilates | Highest: cm of lead / m of concrete |
| Deflection in B-field | Slight (heavy) | Strong (light, −ve) | Strong (light, +ve, opposite to β−) | None (neutral) |
| Example | 238U → 234Th + α | 14C → 14N + β− | 22Na → 22Ne + β+ | Excited 60Ni* → 60Ni + γ |
Memory aid: ionising power α > β > γ; penetrating power γ > β > α (inverse order, the more it ionises, the sooner it stops).
Half-life and Rate of Decay
The number of un-decayed nuclei follows an exponential law:
N = N0·e−λt
where λ is the decay constant (s-1) and N0 is the initial number of nuclei. The half-life t½ is the time for half the nuclei to decay:
t½ = ln(2)/λ = 0.693/λ
Activity A = λN (decays per second; SI unit becquerel, Bq). 1 Ci (curie) = 3.7×1010 Bq.
Successive half-lives
After n half-lives, the fraction remaining is (½)n. So after 1, 2, 3 half-lives we have 50%, 25%, 12.5% left.
Biological and Medical Uses of Radiation
Diagnostic uses
- X-rays: imaging of bones and dense tissues.
- Tc-99m (technetium): SPECT imaging of organs (most widely used medical radioisotope; t½ = 6 h).
- I-131 (iodine): diagnosing and treating thyroid disorders (t½ = 8 days).
- F-18: PET scans (t½ ≈ 110 min).
Therapeutic uses
- Co-60 (cobalt): external-beam radiotherapy for cancer (gamma source).
- I-131: destroys overactive thyroid tissue.
- P-32: treats blood disorders.
Other applications
- C-14 (carbon-14) dating: archaeology, t½ = 5730 years.
- Sterilisation of surgical equipment via gamma rays.
- MRI uses non-ionising radio-frequency fields and is therefore considered safer than CT or X-ray.
Worked MCQs
Five MCQs that capture the high-yield testing patterns for this chapter.
Q1. A radioactive sample has a half-life of 10 days. The fraction left after 30 days is:
30 days = 3 half-lives. Fraction remaining = (½)³ = 1/8.
Q2. When a nucleus undergoes α-decay, its mass number A and atomic number Z change by:
An alpha particle is a 42He nucleus, so A drops by 4 and Z by 2.
Q3. The relation between half-life and decay constant is:
From N = N0e−λt, setting N = N0/2 gives λt½ = ln(2) = 0.693, so t½ = 0.693/λ.
Q4. Which radiation has the greatest penetrating power?
Gamma rays have the highest penetrating power; alpha particles have the highest ionising power but are stopped by a sheet of paper.
Q5. The radioisotope most widely used in diagnostic medical imaging is:
Technetium-99m, with its short 6-hour half-life and pure gamma emission, accounts for ~80% of all nuclear-medicine diagnostic procedures.
Quick Recap
- Nuclide AZX: A = nucleons, Z = protons.
- Binding energy E = Δm·c²; max BE/nucleon at 56Fe.
- α (Z−2, A−4); β− (Z+1); β+ (Z−1); γ (no change).
- N = N0e−λt, t½ = 0.693/λ, A = λN.
- Penetration: γ > β > α; Ionisation: α > β > γ.
- Tc-99m imaging, Co-60 therapy, I-131 thyroid, C-14 dating, MRI is non-ionising.