Q.How many α - particles are emitted by 0.1 g of 226Ra in one year?
(Ans. : 1.154 × 10^17)

The rate of decay of a radioelement -- its activity -- is the number of nuclei decaying per unit time, $-\frac{dN}{dt}$ (the minus sign converts the naturally negative $dN/dt$, since N is shrinking, into a positive activity), measured in disintegrations per second (dps). The first-order rate law states this rate is directly proportional to the number of undecayed nuclei present at that instant: $-\frac{dN}{dt} = \lambda N$, defining the decay constant $\lambda$ as the fraction of nuclei decaying per unit time. Integrating this rate law gives the exponential decay law $N = N_0 e^{-\lambda t}$ …