$A$ radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5\, minutes$,the rate becomes $1250$ disintegrations per minute. Then,its decay constant (per minute) is

$A$ radioactive substance decays to $\left(\frac{1}{16}\right)^{th}$ of its initial activity in $80\, days$. The half-life of the radioactive substance expressed in days is ... .

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 count rate for $10 \, g$ of radioactive material was measured at different times and this has been shown in the graph. The half-life of the material and the total count in the first half-life period respectively are:

$A$ radioactive isotope has a half-life of $T$ years. How long will it take the activity to reduce to $(a)$ $3.125\%$ $(b)$ $1\%$ of its original value?

Half-life of radium is $1620$ years. How many radium nuclei decay in $5$ hours in $5 \, g$ of radium? (Atomic weight of radium $= 223$)