The radioactivity of a certain radioactive element drops to $1/64$ of its initial value in $30 \, s$. Its half-life is ......... $s$.

Half-lives of two radioactive nuclei $A$ and $B$ are $10 \, minutes$ and $20 \, minutes$,respectively. If,initially,a sample has an equal number of nuclei,then after $60 \, minutes$,the ratio of the number of decayed nuclei of $A$ and $B$ will be:

Two radioactive materials $M_1$ and $M_2$ have decay constants $9 \lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. The ratio of the number of nuclei of $M_1$ to that of $M_2$ will be $\frac{1}{e}$ after a time interval of:

If the half-life of radium is $77$ days,its decay constant in $day^{-1}$ will be:

$A$ and $B$ are two radioactive elements. The mixture of these elements shows a total activity of $1200 \text{ disintegrations/minute}$. The half-life of $A$ is $1 \text{ day}$ and that of $B$ is $2 \text{ days}$. What will be the total activity after $4 \text{ days}$? Given,the initial number of atoms in $A$ and $B$ are equal.

$A$ radioactive substance in a laboratory has a half-life of $2 \text{ hours}$. It is considered safe for laboratory use when its activity reduces to $1/64$ of its initial value. After how many hours will the laboratory be safe?