The half-life of a radioactive isotope $X$ is $1.37 \times 10^9 \, y$. It decays to a stable isotope $Y$. In a rock sample from the moon,the ratio of $X$ to $Y$ is $1:7$. The age of the rock is:

The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half-life of the radioactive sample is

$A$ freshly prepared radioactive source of half-life $2\, hours$ emits radiation of intensity which is $64\, times$ the permissible safe level. The minimum time after which it would be possible to work safely with the source is .......... $hours$.

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 $t = 0$?

The decay constant of a radioactive substance is $0.173 \, (years)^{-1}.$ Therefore:

$A$ radioactive element having a half-life of $30 \ min$ is undergoing beta decay. The fraction of the radioactive element that remains undecayed after $90 \ min$ will be: