After $3$ hours,only $0.25 \,mg$ of a pure radioactive material is left. If the initial mass was $2 \,mg$,then the half-life of the substance is ...... $hr$.

Two radioactive elements $R$ and $S$ disintegrate as:
$R \rightarrow P + \alpha; \lambda_R = 4.5 \times 10^{-3} \, \text{years}^{-1}$
$S \rightarrow P + \beta; \lambda_S = 3 \times 10^{-3} \, \text{years}^{-1}$
Starting with the number of atoms of $R$ and $S$ in the ratio of $2:1$,what will be this ratio after the lapse of three half-lives of $R$?

There are three lumps of a given radioactive substance. Their activity is in the ratio of $1 : 2 : 3$ now. What will be the ratio of their activities at any further date?

In a radioactive material,the fraction of active material remaining after time $t$ is $\frac{9}{16}$. The fraction that was remaining after $\frac{t}{2}$ is:

$A$ radioactive substance has a half-life of $10^8$ years and an activity of $10^4 \,Bq$. The number of atoms of this substance present is

If $3/4$ of a radioactive sample decays in $3/4 \, s$,then the half-life of the sample is ........ .