• $summary_{type}$: revision
• $word_{count}$: 180

Essential formulas: R = $R_0$A^$\frac{1}{3}$ ($R_0$ = 1.2 fm). $Delta_m$ = Z$m_p$ + (A-Z)$m_n$ - M. BE = $Delta_m$ x 931.5 MeV. N(t) = $N_0$e^(-lambdat). t_$\frac{1}{2}$ = 0.693/lambda. tau = 1.44t_$\frac{1}{2}$. Activity A = lambda*N. 1 u = 931.5 MeV/$c^2$. Alpha: Z-2, A-4. Beta-minus: Z+1, A same. Gamma: Z same, A same.

JEE strategy by question type: (1) Radius ratio: use R proportional to A^$\frac{1}{3}$. (2) Binding energy: compute mass defect, multiply by 931.5. (3) Decay problems: identify n = \frac{t}{t_}$$\frac{1}{2}; if integer, use $N_0$/2^n; otherwise use exponential. (4) Successive decays: track Z and A through each step. (5) Q-value: sum reactant masses minus product masses, times 931.5. (6) Decay chain: alpha count = $Delta_A$/4, then balance Z for beta count. Common traps: confusing remaining with decayed fraction, forgetting neutrino in beta decay energy sharing, using atomic vs nuclear masses inconsistently, and assuming alpha particle carries all Q-value energy $\frac{it carries only (A-4}{A}$ fraction).