Half-life of a radioactive sample is $24 \,h$. If a newly prepared radioactive sample shows $4$ times the allowed and safe value of radioactivity, the minimum time after which one can work safely with the source is (in $\,h$)

The half-life of radium is $1600 \, \text{years}$. The fraction of the radium sample that will remain after $6400 \, \text{years}$ is:

The half-life of a radioactive isotope $X$ is $50$ years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be:

If $20 \, g$ of a radioactive substance reduces to $10 \, g$ due to radioactive decay in $4 \, minutes$, then in what time will $80 \, g$ of the same substance reduce to $10 \, g$?

In an old rock,the ratio of uranium to lead nuclei is $1:1$. The half-life of uranium is $4.5 \times 10^9$ years. If the rock initially contained only uranium nuclei,how old is the rock?

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