The disintegration rate of a certain radioactive sample at any instant is $4250$ disintegrations per minute. $10$ minutes later,the rate becomes $2250$ disintegrations per minute. The approximate decay constant is $......... \min^{-1}$.

$A$ radioactive sample is an $\alpha$-emitter with a half-life of $138.6$ days. $A$ student observes its activity to be $2000$ disintegrations per second. The number of radioactive nuclei for this given activity is:

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

The half-life of $Bi^{210}$ is $5$ days. If we start with $50,000$ atoms of this isotope,the number of atoms left over after $10$ days is:

The mean lives of a radioactive sample are $30 \, years$ and $60 \, years$ for $\alpha$-emission and $\beta$-emission,respectively. If the sample decays by both $\alpha$-emission and $\beta$-emission simultaneously,then the time after which only one-fourth of the sample remains is approximately ............ $years$.

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.