The radiation emitted by a radioactive substance with a half-life of $30 \ min$ is measured by a Geiger-Muller counter. If the count rate drops to $5 \ \text{disintegrations/sec}$ in $2 \ \text{hours}$, find the initial disintegration rate.

At time $t = 0$,the mass of a radioactive element sample is $10 \, g$. After a time interval equal to two mean lives,what mass of the sample will approximately remain in $g$?

$A$ fresh radioactive sample is given at $t = 0$. Its decay fraction is $\frac{1}{5}$ at $t_1$ instant and $\frac{4}{5}$ at $t_2$ instant. Its mean life is

The half-life of a radioactive element is $1600$ years. The fraction of the sample that remains undecayed after $6400$ years will be:

$A$ radioactive element $ThA$ $(_{84}Po^{216})$ can undergo $\alpha$ and $\beta$ types of disintegrations with half-lives $T_1$ and $T_2$ respectively. Then the effective half-life of $ThA$ is:

$A$ certain radioactive element disintegrates with a decay constant of $7.9 \times 10^{-10} / s$. At a given instant of time, if the activity of the sample is equal to $55.3 \times 10^{11}$ disintegration/second, then the number of nuclei at that instant of time is: