Nuclear Chemistry & Radioactivity: JEE Main Guide

Nuclear chemistry — radioactivity, half-life, nuclear reactions, binding energy, and radioactive decay series — contributes one to two questions per JEE Main session. The chapter is formula-compact: one decay law, one half-life formula, and the binding energy concept cover 80% of all questions. This guide makes these concepts exam-ready in a single focused session.

Radioactive Decay Law

Radioactive decay is first-order: N = N₀e^(−λt), where N₀ is the initial number of nuclei, N is the number remaining at time t, and λ is the decay constant. Half-life: t₁/₂ = ln2/λ = 0.693/λ. Mean life: τ = 1/λ = t₁/₂/0.693 ≈ 1.44 × t₁/₂. Activity A = λN = (0.693/t₁/₂) × N. Units of activity: Becquerel (Bq) = 1 disintegration per second; Curie (Ci) = 3.7 × 10¹⁰ Bq.

Number of nuclei after n half-lives: N = N₀ × (1/2)ⁿ. JEE Main uses this in two ways: (1) given t₁/₂ and total time t, find n = t/t₁/₂, then N = N₀/2ⁿ; (2) given that activity has fallen to a fraction (e.g., 1/8 of original), find n: (1/2)ⁿ = 1/8 → n = 3, so t = 3t₁/₂. For the parallel in Physics, see our Nuclear Physics Guide.

Alpha, Beta, and Gamma Decay

Alpha decay (²⁴He emission): mass number decreases by 4, atomic number decreases by 2. Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He. Beta-minus decay (electron emission): neutron converts to proton, so mass number unchanged, atomic number increases by 1. Beta-plus decay (positron emission): proton converts to neutron, atomic number decreases by 1. Gamma decay: no change in A or Z, only energy released. JEE Main tests balancing nuclear equations — apply conservation of mass number and atomic number. Take a free mock test on nuclear chemistry to practise decay balancing and half-life calculations.

Binding Energy and Nuclear Stability

Mass defect Δm = (Z × m_p + N × m_n) − m_nucleus. Binding energy BE = Δm × c² (in MeV: multiply Δm in amu by 931.5 MeV/amu). Binding energy per nucleon (BE/A) is the stability indicator: higher BE/A means more stable nucleus. Maximum BE/A occurs around A = 56 (iron-56 — most stable nucleus). Light nuclei (A < 56) gain stability by fusion; heavy nuclei (A > 56) gain stability by fission. This is the origin of both nuclear fusion (stars) and nuclear fission (reactors).

JEE Main tests: calculate the energy released in fission or fusion given the mass defect. Q-value = (initial mass − final mass) × 931.5 MeV. If Q > 0, energy is released (exothermic); if Q < 0, energy must be input (endothermic). The fission of U-235 by slow neutrons: ²³⁵U + n → ²³⁶U → fission products + 2-3 neutrons + ~200 MeV per fission. Chain reaction possible because each fission produces more neutrons.

Radioactive Series

Three natural decay series: uranium series (starts at ²³⁸U, ends at ²⁰⁶Pb), actinium series (²³⁵U → ²⁰⁷Pb), and thorium series (²³²Th → ²⁰⁸Pb). A fourth artificial series (neptunium) starts at ²³⁷Np. JEE Main asks: starting at a given nucleus, after α and β decays, identify the final nucleus. Count: each α decreases A by 4 and Z by 2; each β decreases A by 0 and increases Z by 1. Track both A and Z through the decay chain.

Carbon-14 Dating

¹⁴C is produced in the upper atmosphere by cosmic ray bombardment of ¹⁴N: ¹⁴N + n → ¹⁴C + p. Living organisms maintain constant ¹⁴C/¹²C ratio by exchanging carbon with the atmosphere. When an organism dies, the ratio decreases due to ¹⁴C decay. t₁/₂ of ¹⁴C = 5730 years. Age of a sample: t = (t₁/₂/0.693) × ln(N₀/N) where N₀/N is the ratio of original to present ¹⁴C activity. JEE Main occasionally tests the calculation of carbon-14 age from the fraction of original activity remaining.

Exam Strategy

Nuclear chemistry requires accurate nuclear equation balancing and confident half-life calculations. For balancing: always conserve both A (mass number) and Z (atomic number). For half-life: always find n = t/t₁/₂ first, then compute. The binding energy questions are less frequent but high-marks when they appear — know BE = Δm × 931.5 MeV (in amu) and which element has maximum stability (⁵⁶Fe). For complete modern chemistry, pair with our Modern Physics Guide. Upgrade for ₹149/month for nuclear chemistry and radioactivity chapter tests.