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

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

The half-life of a radioactive substance is $48$ hours. How much time will it take to disintegrate to its $\frac{1}{{16}} \,th$ part ............$hour$

At time $t=0$, a container has $N_{0}$ radioactive atoms with a decay constant $\lambda$. In addition, $c$ numbers of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at $t=T$ ?

For a certain radioactive process the graph between $In\, {R}$ and ${t}\,({sec})$ is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately $....\,{sec}.$

If $'f^{\prime}$ denotes the ratio of the number of nuclei decayed $\left(N_{d}\right)$ to the number of nuclei at $t=0$ $\left({N}_{0}\right)$ then for a collection of radioactive nuclei, the rate of change of $'f'$ with respect to time is given as:

$[\lambda$ is the radioactive decay constant]