The ratio of the number of active nuclei of two different radioactive samples is $2:3$. Their half-lives are $1 \ h$ and $2 \ h$ respectively. The ratio of the number of active nuclei after $6 \ h$ will be:

The decay constant of a radioisotope is $\lambda$. If $A_1$ and $A_2$ are its activities at times $t_1$ and $t_2$ respectively,what is the number of nuclei that have decayed during the time interval $(t_1 - t_2)$?

An accident in a nuclear laboratory resulted in the deposition of a certain amount of radioactive material with a half-life of $18$ days inside the laboratory. Tests revealed that the radiation level was $64$ times higher than the permissible level required for safe operation. What is the minimum number of days after which the laboratory can be considered safe for use?

$A$ fresh radioactive sample is given at $t = 0$. Its decay fraction is $\frac{1}{5}$ at $t_1$ instant and $\frac{4}{5}$ at $t_2$ instant. Its mean life is

If the radioactive decay constant of radium is $1.07 \times 10^{-4}$ per year,then its half-life period is approximately equal to ......... $years$.

$1 \, mg$ of gold undergoes decay with a $2.7 \, \text{days}$ half-life period. The amount left after $8.1 \, \text{days}$ is ......... $mg$.