The half-life of a radioactive substance is $3.6$ days. How much of $20\, mg$ of this radioactive substance will remain after $36$ days?

The initial activity of a certain radioactive isotope was measured as $16000 \ counts \ min^{-1}$. Given that the only activity measured was due to this isotope and that its activity after $12 \ h$ was $2000 \ counts \ min^{-1}$,its half-life,in hours,is nearest to

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5$ minutes. The time (in minutes) at which the activity reduces to half its value 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 $8 \ hr$,what is the ratio of their rates of disintegration?

Activity of a radioactive sample is $R_1$ at a time $t_1$ and $R_2$ at a time $t_2$. Its half-life period is $T$. The number of atoms that have disintegrated in the time interval $(t_2 - t_1)$ is equal to $\frac{n(R_1 - R_2)T}{\ln 4}$. Then '$n$' is equal to

The half-lives of a radioactive substance are $T$ and $2T$ years for $\alpha$-emission and $\beta$-emission,respectively. The total decay constant for the simultaneous decay of the $\alpha$ and $\beta$ radioactive substance is: