• $summary_{type}$: application
• $word_{count}$: 170

The decay law N(t) = $N_0$e^(-lambdat) describes the exponential decrease in number of undecayed nuclei. Activity A(t) = lambdaN(t) = $A_0$e^(-lambdat) measures decays per second. Half-life t_$\frac{1}{2}$ = 0.693/lambda is the time for N to halve. Mean life tau = 1/lambda = 1.44t_$\frac{1}{2}$ is the average lifetime per nucleus. After n half-lives: N = $N_0$/2^n, fraction decayed = 1 - 1/2^n (common trap: confusing remaining with decayed). For non-integer half-lives, use the exponential form. Activity units: 1 Bq = 1 decay/s, 1 Ci = 3.7 x 10^10 Bq. JEE numerical strategy: if the time is a simple multiple of half-life, use N = $N_0$/2^n directly; otherwise use the exponential. For finding time to reach a given fraction: t = $\frac{t_(1/2}{0.693}$)*ln$\frac{N_0}{N}$. The activity of a freshly prepared sample increases if a parent is producing the isotope (Bateman equations).