Alpha, Beta & Gamma Decay: JEE Main Guide

Nuclear decay is a favourite JEE topic because the questions are formulaic, the concepts are clean, and students who learn the conservation rules can answer questions that look complicated in under 60 seconds. This guide covers the three types of radioactive decay, the conservation laws that govern each, penetration and ionisation properties, and the decay series problems that appear every few sessions.

Alpha Decay

In alpha (α) decay, the parent nucleus emits a helium-4 nucleus (₂⁴He). Conservation of mass number A and atomic number Z: ᴬ_Z X → ᴬ⁻⁴_(Z−2) Y + ₂⁴He. Mass number decreases by 4; atomic number decreases by 2. Example: ²³⁸₉₂U → ²³⁴₉₀Th + ₂⁴He. Alpha particles are the heaviest decay product; they are emitted with discrete (quantised) kinetic energies corresponding to specific nuclear energy levels. Alpha radiation has the highest ionising power (doubly charged, slow) and the shortest range in matter (~5 cm in air, stopped by a sheet of paper). Tunnelling through the Coulomb barrier explains why alpha decay occurs even when classically forbidden — a direct application of quantum mechanics that JEE tests in Modern Physics.

Q-value: Q = (M_parent − M_daughter − M_alpha) × c². For decay to be spontaneous, Q > 0. The kinetic energy of the alpha particle ≈ Q × M_daughter/(M_alpha + M_daughter) (by conservation of momentum, recoil energy of daughter = Q − KE_alpha). Take a free nuclear physics mock. See our nuclear binding energy guide for Q-value derivations.

Beta Decay: Two Types

Beta-minus (β⁻) decay: a neutron converts to a proton, emitting an electron and an antineutrino. ᴬ_Z X → ᴬ_(Z+1) Y + e⁻ + ν̄_e. Mass number unchanged; atomic number increases by 1. Beta-plus (β⁺) decay: a proton converts to a neutron, emitting a positron and a neutrino. ᴬ_Z X → ᴬ_(Z−1) Y + e⁺ + ν_e. Mass number unchanged; atomic number decreases by 1. The neutrino (nearly massless, uncharged) was postulated by Pauli to explain why beta particles have a continuous energy spectrum (not discrete like alpha particles) — the energy is shared between the electron and neutrino.

Electron capture: an inner orbital electron is captured by the nucleus, converting a proton to a neutron. Same net effect as β⁺ but no positron emitted. JEE tests the identification of decay type from the change in Z and A, and the identification of the decay product. Beta particles have intermediate ionising power and range (~1 m in air, stopped by a few mm of aluminium).

Gamma Decay and Nuclear Energy Levels

Gamma (γ) decay occurs when a nucleus in an excited state drops to a lower energy state, emitting a high-energy photon (γ ray). No change in A or Z. Gamma rays have the lowest ionising power but the highest penetrating power — they require several centimetres of lead or metres of concrete to reduce intensity by half. Half-value layer (HVL): thickness of absorber that reduces intensity to half. Gamma radiation follows exponential attenuation: I = I₀ e^(−μx) where μ is the linear attenuation coefficient.

Decay Series and Combined Decays

Starting from ²³⁸₉₂U, the decay series to stable ²⁰⁶₈₂Pb involves 8 alpha decays and 6 beta-minus decays. JEE question type: given a parent nucleus undergoes x alpha decays and y beta decays to reach a stable daughter, find x and y. Method: change in A = 4x → x = ΔA/4. Change in Z = 2x − y → y = 2x − ΔZ. Example: ²³⁸₉₂U → ²⁰⁶₈₂Pb: ΔA = 32, x = 8 alpha decays. ΔZ = 10, y = 2(8) − 10 = 6 beta decays. This template solves every decay-series question in the exam. For radioactivity kinetics (half-life, activity), see our nuclear radioactivity guide and our nuclear physics guide.