The half-life $(T)$ and the disintegration constant $(\lambda)$ of a radioactive substance are related as:

Two radioactive elements $A$ and $B$ initially have the same number of atoms. The half-life of $A$ is equal to the mean life of $B$. If $\lambda_A$ and $\lambda_B$ are the decay constants of $A$ and $B$ respectively,then choose the correct relation from the given options.

Ten percent of a radioactive sample has decayed in $1$ day. After $2$ days,the decayed percentage of nuclei will be ...... $\%$

Two radioactive samples $A$ and $B$ have half-lives $T_1$ and $T_2$ $(T_1 > T_2)$ respectively. At $t=0$,the activity of $B$ was twice the activity of $A$. Their activity will become equal after a time:

The activity of a radioactive sample is $9750$ counts/minute at $t = 0$ and $975$ counts/minute at $t = 5$ minutes. The decay constant is .......... $min^{-1}$.

The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second,whose mean life is $10^9 \ s$. The mass of an atom of this radioisotope is $10^{-25} \ kg$. The mass (in $mg$) of the radioactive sample is