Nuclear Radioactivity for JEE Main: Complete Guide

Nuclear physics and radioactivity contribute three to four questions in every JEE Main session, and most of them are straightforward once the decay rules, the radioactive decay law, and binding energy calculations are internalised. The chapter rewards precision over creativity — know the formulas cold and the marks come reliably.

Alpha, Beta, and Gamma Decay Rules

In alpha decay (emission of ⁴₂He): mass number decreases by 4, atomic number by 2. In beta-minus decay (emission of electron, ⁰₋₁e): mass number unchanged, atomic number increases by 1. In beta-plus decay (positron emission): atomic number decreases by 1. In electron capture: atomic number decreases by 1, just like beta-plus but no positron emitted. Gamma decay: no change in A or Z — the nucleus just releases energy. JEE problems on decay chains require applying these rules sequentially; track A and Z for each step. See the nuclear binding context in our nuclear physics guide.

The Radioactive Decay Law

N(t) = N₀ e^(−λt) = N₀ (1/2)^(t/t½), where λ is the decay constant and t½ = ln2/λ = 0.693/λ is the half-life. Activity A = λN = A₀ (1/2)^(t/t½). After n half-lives, the fraction remaining is (1/2)ⁿ. After 10 half-lives, less than 0.1% of the original sample remains. A common JEE question: if activity drops from A₀ to A₀/32 in 100 days, what is the half-life? Answer: 100/5 = 20 days (since 32 = 2⁵). This pattern — equating the ratio to a power of 2 — solves every such question instantly.

Mean Life and Activity

The mean life τ = 1/λ = t½/0.693 ≈ 1.44 t½. After time τ, the number remaining is N₀/e ≈ 37% of the original. Activity (disintegrations per second) is measured in Becquerel (1 Bq = 1 decay/s) or Curie (1 Ci = 3.7 × 10¹⁰ Bq). JEE problems involving activity and mean life are among the most predictable in the chapter, almost always reducible to A = λN₀ followed by reading off from the decay law.

Binding Energy and Mass Defect

The mass defect Δm = [Z·m_p + (A−Z)·m_n − M_nucleus]. Binding energy BE = Δm × 931.5 MeV/u. The binding energy per nucleon BE/A peaks around A = 56 (iron) at ~8.8 MeV and decreases for both lighter and heavier nuclei, explaining why fusion of light nuclei and fission of heavy nuclei both release energy. JEE asks for the Q-value of reactions: Q = (mass of reactants − mass of products) × 931.5 MeV/u. A positive Q means energy is released.

Fission, Fusion, and Q-Value Problems

In fission of ²³⁵U, the total binding energy of products exceeds that of the parent, releasing ~200 MeV per reaction. In fusion of deuterium and tritium to helium-4, the binding energy gain is ~17.6 MeV. These figures are worth memorising for quick conceptual questions. Q-value problems give you the atomic masses and ask for the energy released — apply Q = Δm × 931.5 MeV/u. After practising these calculations, take a free mock test on modern and nuclear physics for a consolidated assessment.