In a radioactive disintegration,the ratio of the initial number of atoms to the number of atoms present at an instant of time equal to its mean life is:

Plutonium decays with a half-life of $24000 \, \text{years}$. If the plutonium is stored for $72000 \, \text{years}$, then the fraction of plutonium that remains is

$A$ radioactive nucleus can decay in two different processes with half-lives of $0.7 \ hr$ and $0.3 \ hr$. The effective average life of the nucleus in minutes is approximately (value of $\ln 2 = 0.7$):

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 $R$?

If $M_0$ is the initial mass of a radioactive substance with a half-life of ${t_{1/2}} = 5 \text{ years}$,what is the amount of substance remaining after $15 \text{ years}$?

If $T$ is the half-life of a radioactive material,then the fraction that would remain after a time $\frac{T}{2}$ is