$A$ sample of a radioactive element has a mass of $10 \, g$ at an instant $t = 0$. The approximate mass of this element in the sample after two mean lives is .......... $g$.

Let $N_{\beta}$ be the number of $\beta$ particles emitted by $1 \, g$ of $^{24}Na$ radioactive nuclei (half-life $= 15 \, hrs$) in $7.5 \, hrs$. $N_{\beta}$ is close to (Avogadro number $= 6.023 \times 10^{23} \, mol^{-1}$)

The half-life of a radioactive nucleus is $50$ days. The time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it had decayed and the time $t_1$ when $\frac{1}{3}$ of it had decayed is (in days):

The graph in the figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t$. The relationship between $A$ and $t$ is (Assume $\ln 12 = 2.6$):

Mean life of a radioactive sample is $100$ seconds. Then its half-life (in minutes) is

The activity of a sample of radioactive material is $A_1$ at time $t_1$ and $A_2$ at time $t_2$ $(t_2 > t_1)$. Its mean life is $T$.