The half-life period of element $X$ is same as the mean life time of element $Y$. Assume initially $X$ and $Y$ have same number of atoms. Then

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:

$A$ freshly prepared radioactive source of half-life $2\, hours$ emits radiation of intensity which is $64\, times$ the permissible safe level. The minimum time after which it would be possible to work safely with the source is .......... $hours$.

The radioactivity of a sample is $R_1$ at a time $T_1$ and $R_2$ at a time $T_2$. If the half-life of the specimen is $T$,then the number of atoms that have disintegrated in the time interval $(T_2 - T_1)$ is proportional to

Two radioactive materials $X_1$ and $X_2$ 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 $X_1$ to that of $X_2$ will be $1 / e$ after a time:

$A$ piece of wood from a recently cut tree shows $20$ decays per minute. $A$ wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows $2$ decays per minute. If the half-life of $C^{14}$ is $5730$ years,then the age of the wooden piece placed in the museum is approximately ........... years.