Nuclear Reactions & Radioactive Decay: JEE Main Guide

Nuclear physics is one of the highest return-on-investment topics in JEE Main Physics. It contributes three to five questions per session, the formula count is low, and the question types are highly predictable. A focused week on this chapter can reliably secure 12 to 15 marks that many students leave behind by neglecting it. This guide covers every concept JEE actually tests.

Nuclear Size, Mass Defect, and Binding Energy

The nuclear radius follows R = R₀A^(1/3), where R₀ ≈ 1.2 fm and A is the mass number. This R³ ∝ A relation means nuclear density is approximately constant at 2.3×10¹⁷ kg/m³ regardless of which element — a remarkable fact that JEE tests directly. The mass defect Δm = (Zm_p + Nm_n) − M_nucleus is the mass converted to binding energy via E = Δmc². The binding energy per nucleon (BE/A) peaks around iron-56 and decreases for both lighter and heavier nuclei.

The BE/A curve drives nuclear energy release: fission of heavy nuclei (uranium) moves toward the peak, releasing energy; fusion of light nuclei (hydrogen) also moves toward the peak, releasing even more energy per nucleon. A question giving the mass defect and asking for energy released is direct: convert Δm in atomic mass units to MeV using 1 u = 931.5 MeV/c². Confirm your speed with a free nuclear physics mock.

Radioactive Decay Law and Half-Life

The number of radioactive nuclei decreases as N(t) = N₀e^(−λt), where λ is the decay constant. The half-life T½ = ln2/λ ≈ 0.693/λ is the time for half the nuclei to decay. The mean lifetime τ = 1/λ = T½/ln2 ≈ 1.44 T½ is slightly longer than the half-life. JEE frequently asks: how many nuclei remain after n half-lives (answer: N₀/2ⁿ), or what fraction remains after a given time (use the exponential formula).

The activity A = λN = A₀e^(−λt) decays with the same law. A quantity that decays to 1/8 of its initial value has gone through 3 half-lives (since 2³ = 8). Recognising these simple multiples of half-life is faster than using the exponential formula and applies to 70% of activity questions. Nuclear decay modes: alpha decay decreases A by 4 and Z by 2; beta-minus decay increases Z by 1; beta-plus decay decreases Z by 1; gamma decay changes neither A nor Z. Tracking Z and A through a decay sequence is a standard 3-mark question type.

Fission, Fusion, and Nuclear Reactions

In nuclear reactions, mass number A and atomic number Z are both conserved, as is charge. Given a reaction equation with one unknown particle, use these conservation laws to identify it. For example, given ⁹₄Be + X → ¹²₆C + ¹₀n, conservation gives X as ⁴₂He (an alpha particle). This identification type accounts for one question per session reliably.

The Q-value of a reaction = (mass of reactants − mass of products)c². Positive Q means energy is released (exothermic); negative Q means energy must be supplied (endothermic). Fission reactions have Q ≈ 200 MeV per fission event; fusion reactions have Q ≈ 17.6 MeV per deuterium-tritium fusion — but fusion releases more energy per unit mass because the mass of the fuel is so much smaller. For the broader modern physics context that this chapter belongs to, see our semiconductor devices guide and the Physics 100+ strategy. Complete this chapter alongside our last-minute revision guide for maximum exam-day readiness.