Age of a tree is determined using radio-isotope of

The half life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y$. Initially both of them have the same number of atoms. Then

Half life of $B{i^{210}}$ is $5$ days. If we start with $50,000$ atoms of this isotope, the number of atoms left over after $10$ days is

The plot of the number $(N)$ of decayed atoms versus activity $(A)$ of a radioactive substance is

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

The count rate of a Geiger- Muller counter for the radiation of a radioactive material of half life of $30\, minutes$ decreases to $5\,{s^{ - 1}}$ after $2\, hours.$ The initial count rate was..........${s^{ - 1}}$