The half-life of a particle of mass $1.6 \times 10^{-26} \,kg$ is $6.9 \,s$. $A$ stream of such particles is travelling with a kinetic energy of $0.05 \,eV$ per particle. The fraction of particles that will decay when they travel a distance of $1 \,m$ is

$A$ 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 effective 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? (in years)

$A$ radioactive isotope $X$ with a half-life of $1.37 \times 10^9$ years decays to $Y$,which is stable. $A$ sample of rock from the moon was found to contain both the elements $X$ and $Y$ in the ratio of $1 : 7$. The age of the rock is

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

For a radioactive material,the half-life is $10$ minutes. If initially there are $600$ nuclei,the time taken (in minutes) for the disintegration of $450$ nuclei is:

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):