The radioactive sources $A$ and $B$ of half lives of $2\, hr$ and $4\, hr$ respectively, initially contain the same number of radioactive atoms. At the end of $2\, hours,$ their rates of disintegration are in the ratio :

A radioactive material of half-life $T$ was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If now their present activities are $A_1$ and $A_2$ respectively then their age difference equals :

A radioactive sample has ${N_0}$ active atoms at $t = 0$. If the rate of disintegration at any time is $R$ and the number of atoms is $N$, then the ratio $ R/N$ varies with time as

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

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]

The radioactivity of a certain radioactive elements drops to $\frac{1}{64}$ of its initial value in $30$ seconds. Its half life is ............. seconds