The half-life of a radioactive element which has only $\frac{1}{32}$ of its original mass left after a lapse of $60\, days$ is ........ $days$.

Two radioactive substances $A$ and $B$ have the same number of initial nuclei. If the half-lives of $A$ and $B$ are $1.5 \ days$ and $4.5 \ days$ respectively, then the ratio of the number of nuclei remaining in $A$ and $B$ after $9 \ days$ is

Two radioactive materials $A$ and $B$ have decay constants $10\lambda$ and $\lambda$,respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $A$ to that of $B$ will be $1/e$ after a time:

$A$ radioactive nucleus can decay by two different processes. The half-life for the first process is $3.0 \, hours$ while it is $4.5 \, hours$ for the second process. The effective half-life of the nucleus will be $......... \, hours.$

$A$ radioactive material has a half-life of $10$ days. What fraction of the material would remain after $30$ days?

$N$ atoms of a radioactive element emit $n$ alpha particles per second. The half-life of the element is: