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 sample of a given rock. The age of the rock is estimated to be:

$A$ certain radioactive substance reduces to $25\%$ of its initial value in $16\ days$. Its half-life is .......... $days$.

$A$ sample of radioactive material has mass $m$,decay constant $\lambda$,and molar mass $M$. If the Avogadro constant is $N_A$,what is the initial activity of the sample?

If ${N_0}$ is the original mass of the substance of half-life period ${T_{1/2}} = 5 \text{ years}$,then the amount of substance left after $15 \text{ years}$ is

Half-lives of two radioactive elements $A$ and $B$ are $30 \text{ minute}$ and $60 \text{ minute}$ respectively. Initially,the samples have an equal number of nuclei. After $120 \text{ minute}$,the ratio of the number of decayed nuclei of $B$ to that of $A$ will be:

The relation between $\lambda$ and $T_{1/2}$ is ($T_{1/2} = \text{half-life}$,$\lambda = \text{decay constant}$)