At a given instant,there are $25\%$ undecayed radioactive nuclei in a sample. After $10 \, s$,the number of undecayed nuclei reduces to $6.25\%$. The mean life of the nuclei is...........$ s$.

What is the half-life (in years) of a radioactive material if its activity drops to $1/16$th of its initial value in $30$ years (in $.5$)?

The decay constant of radium is $\lambda$. By a suitable process,its compound radium bromide is obtained. The decay constant of radium bromide will be:

The half-life of a radioactive substance is $T$. The time taken for all the nuclei to disintegrate will be

$A$ radioactive element $X$ converts into another stable element $Y$. The half-life of $X$ is $2 \text{ hours}$. Initially,only $X$ is present. After a time $t$,if the ratio of atoms of $X$ to $Y$ is $1:4$,then the value of $t$ is

$A$ 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: