In a radioactive disintegration,the ratio of the initial number of atoms to the number of atoms present at an instant of time equal to its mean life is:

The half-life of $^{215}At$ is $100 \,\mu s$. After how much time (in $\mu s$) will $1/16^{th}$ of the sample remain undecayed?

$A$ parent nucleus $X$ decays into a daughter nucleus $Y$,which in turn decays into $Z$. The half-lives of $X$ and $Y$ are $40000 \, yr$ and $20 \, yr$,respectively. In a certain sample,it is found that the number of $Y$ nuclei hardly changes with time. If the number of $X$ nuclei in the sample is $4 \times 10^{20}$,the number of $Y$ nuclei present in it is

$A$ radioactive material of half-life $T$ was kept in a nuclear reactor at two different instants. The quantity kept the second time was twice that kept the first time. If their present activities are $A_1$ (first) and $A_2$ (second) respectively,then their age difference is equal to:

$A$ radioactive sample decays $\frac{7}{8}$ times its original quantity in $15$ minutes. The half-life of the sample is $......$ minutes.

An alloy is composed of two radioactive materials $A$ and $B$ having equal weight. The half-lives of $A$ and $B$ are $10 \ yrs$ and $20 \ yrs$ respectively. After time $t$,the alloy was found to consist of $(1/e) \ kg$ of $A$ and $1 \ kg$ of $B$. If the atomic weights of $A$ and $B$ are the same,then the value of $t$ is (Assume $\ln 2 = 0.7$):