The half-life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y$. Initially,they have the same number of atoms. Then:

The half-life of radium is about $1600$ years. Of $100 \, g$ of radium existing now, $25 \, g$ will remain unchanged after .......... $years$.

Substance $A$ has an atomic mass number of $16$ and a half-life of $1$ day. Another substance $B$ has an atomic mass number of $32$ and a half-life of $0.5$ day. If both $A$ and $B$ start undergoing radioactivity simultaneously with an initial mass of $320 \, g$ each,how many total atoms of $A$ and $B$ combined would be left after $2$ days? (Answer in $......... \times 10^{24}$)

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

If the decay or disintegration constant of a radioactive substance is $\lambda$,then its half-life and mean life are respectively:

The half-life of a radioactive substance is $10 \, \text{minutes}$. If $n_1$ and $n_2$ are the number of atoms decayed in $20 \, \text{minutes}$ and $30 \, \text{minutes}$ respectively, then $n_1 : n_2 =$