Q.Disintegration rate of a radio-active sample is $10^{10}$ per hour at 20 hours from the start. It reduces to $5 \times 10^{9}$ per hour after 30 hours. Calculate the decay constant.

While an individual radioactive nucleus's decay moment is fundamentally unpredictable, a large POPULATION of identical nuclei obeys a precise statistical law. Assuming the number of decays $dN$ in a short interval dt is proportional both to the interval length and to the number of parent nuclei currently present gives the governing equation $\frac{dN}{dt}=-\lambda N(t)$, where $\lambda$, the decay constant, is a fixed property of the particular radioactive species (its intrinsic per-nucleus decay probability per unit time). …