The sample of a radioactive substance has $10^6$ nuclei. Its half-life is $20 \, s$. The number of nuclei that will be left after $10 \, s$ is nearly ...... $\times 10^5$.

The half-life of a radioactive nucleus is $50$ days. The time interval $(t_2 - t_1)$ between the time $t_2$ when $2/3$ of it has decayed and the time $t_1$ when $1/3$ of it has decayed is ...... days.

The activity of a radioactive sample reduces from $A_0$ to $\frac{A_0}{\sqrt{3}}$ in $1$ hour. What will be the activity after $3$ hours more?

$A$ radioactive sample decays by two modes: $\alpha$-decay and $\beta$-decay. $66.6 \%$ of the time it decays by $\alpha$-decay and $33.3 \%$ of the time it decays by $\beta$-decay. If the half-life of the sample is $60 \text{ years}$,what will be the half-life of the sample if it decays only by $\alpha$-decay?

$A$ radioactive sample is undergoing $\alpha$ decay. At any time $t_{1}$,its activity is $A$ and at another time $t_{2}$,the activity is $\frac{A}{5}$. What is the average life time for the sample?

The decay constant of a radioactive element is $0.01 \ s^{-1}$. Its half-life period is ....... $s$.