$A$ heavy nucleus $Q$ of half-life $20 \text{ minutes}$ undergoes alpha-decay with a probability of $60 \%$ and beta-decay with a probability of $40 \%$. Initially,the number of $Q$ nuclei is $1000$. The number of alpha-decays of $Q$ in the first one hour is:

$A$ freshly prepared sample of a radioisotope of half-life $1386 \ s$ has activity $10^3$ disintegrations per second. Given that $\ln 2 = 0.693$,the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first $80 \ s$ after preparation of the sample is:

The half-life of a radioactive substance is $20$ minutes. The difference between the points of time when it is $33\%$ disintegrated and $67\%$ disintegrated is approximately ......... $min$.

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

The activity of a radioactive sample is $64 \times 10^{-5} \text{ Ci}$. Its half-life is $3 \text{ days}$. The activity will become $5 \times 10^{-6} \text{ Ci}$ after how many days?

In a mean life of a radioactive sample,