Nuclear Physics
Nuclear Physics studies the nucleus — its composition, the radiation it emits, and the rules governing radioactive decay. The PMDC MDCAT 2026 syllabus emphasises nuclide notation, half-life calculations, and medical/biological applications. Expect 1-2 MCQs per paper.
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.