Two radioactive materials $A$ and $B$ have decay constants $10\lambda$ and $\lambda$,respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $A$ to that of $B$ will be $1/e$ after a time:

Two radioactive nuclei $P$ and $Q$ in a given sample decay into a stable nucleus $R.$ At time $t = 0,$ the number of $P$ species is $4N_0$ and that of $Q$ is $N_0.$ The half-life of $P$ is $1 \text{ minute},$ while that of $Q$ is $2 \text{ minutes}.$ Initially,there are no nuclei of $R$ present in the sample. When the number of nuclei of $P$ and $Q$ are equal,the number of nuclei of $R$ present in the sample would be

The half-life period of element $X$ is same as the mean life time of element $Y$. Assume initially $X$ and $Y$ have same number of atoms. Then

$A$ source contains two phosphorus radionuclides $_{15}^{32} P \left(T_{1/2} = 14.3 \ d\right)$ and $_{15}^{33} P \left(T_{1/2} = 25.3 \ d\right)$. Initially,$10\%$ of the decays come from $_{15}^{33} P$. How long must one wait until $90\%$ of the decays come from $_{15}^{33} P$?

The activity of a sample is $64 \times 10^{-5} \, Ci$. Its half-life is $3 \, days$. The activity will become $5 \times 10^{-6} \, Ci$ after ......... $days$.

Activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at time $t_2$ $(t_2 > t_1)$. Then the ratio $\frac{R_2}{R_1}$ is: