The half-life of a radioactive element $X$ is equal to the mean life of another radioactive element $Y$. Initially, the number of atoms for both is the same. Then:

The half-life of a radioactive substance is $30 \text{ minutes}$. The time taken between $40 \%$ decay and $85 \%$ decay of the same radioactive substance is

There are two radionuclei $A$ and $B.$ $A$ is an alpha emitter and $B$ is a beta emitter. Their disintegration constants are in the ratio of $1 : 2.$ What should be the ratio of the number of atoms of the two at time $t = 0$ so that the probabilities of getting $\alpha$ and $\beta$ particles are the same at time $t = 0$?

Half-life of a radioactive substance is $20 \ min$. The difference between the points of time when it is $33\%$ disintegrated and $67\%$ disintegrated is approximately ........... $min$.

$A$ radioactive sample consists of two distinct species having an equal number of $N_0$ atoms initially. The mean-life of one species is $\tau$ and of the other is $5\tau$. The decay products in both cases are stable. The total number of radioactive nuclei at $t = 5\tau$ is

The radioactivity of a sample is $R_1$ at a time $T_1$ and $R_2$ at a time $T_2$. If the half-life of the specimen is $T$,then the number of atoms that have disintegrated in the time interval $(T_2 - T_1)$ is proportional to