After two hours, one-sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half-life of the isotope is:

Two radioactive materials $A$ and $B$ have decay constants $25 \lambda$ and $16 \lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $B$ to that of $A$ will be $e$ after a time $t = \frac{1}{a \lambda}$. The value of $a$ is $......$

$A$ radioactive substance contains $10000$ nuclei and its half-life period is $20$ days. The number of nuclei present at the end of $10$ days is

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

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

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: