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

If a radioactive material remains $25 \%$ after $16$ days, then its half life will be ……… days

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

The half life of a radioactive isotope $'X'$ is $20$ years, It decays to another element $'Y'$ which is stable. The two elements $'X'$ and $'Y'$ were found to be in  the ratio $1:7$ in a simple of a given rock . The age of the rock is estimated to be…………$years$