In a radioactive decay process, the activity is defined as $A=-\frac{\mathrm{d} N}{\mathrm{~d} t}$, where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources, $S_1$ and $S_2$ have same activity at time $t=0$. At a later time, the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$, respectively. When $S_1$ and $S_2$ have just completed their $3^{\text {rd }}$ and $7^{\text {th }}$ half-lives, respectively, the ratio $A_1 / A_2$ is. . . . . . .

In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at an instant of time equal to its mean life is

The average life $T$ and the decay constant $\lambda $ of a radioactive nucleus are related as

The half-life of a radioactive substance is $30$ minutes. The times (in minutes ) taken between $40\%$ decay and $85\%$ decay of the same radioactive substance is

At time $t = 0, N_1$ nuclei of decay constant $\lambda _1 \,\& \,N_2$ nuclei of decay constant $\lambda _2$ are mixed . The decay rate of the mixture is :

Unit of radioactivity is Rutherford. Its value is