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. . . . . . .

The half-life of radioactive Polonium $(Po)$ is $138.6$ days. For ten lakh Polonium atoms, the number of disintegrations in $24$ hours is

${ }_{92}^{238} U$ is known to undergo radioactive decay to form ${ }_{82}^{206} Pb$ by emitting alpha and beta particles. A rock initially contained $68 \times 10^{-6} g$ of ${ }_{92}^{238} U$. If the number of alpha particles that it would emit during its radioactive decay of ${ }_{92}^{238} U$ to ${ }_{82}^{206} Pb$ in three half-lives is $Z \times 10^{18}$, then what is the value of $Z$?

Unit of radioactivity is Rutherford. Its value is

If the decay or disintegration constant of a radioactive substance is $\beta $, then its half life and mean life are respectively 

$(log_e \,2 =ln\, 2)$

If a radioactive element having half-life of $30\,min$ is undergoing beta decay, the fraction of radioactive element remains undecayed after $90\,min$. will be :