The half-life of radium is $1600$ years. Its mean life will be ....... years.

$A$ radioactive nucleus decays by two different processes. The half-life of the first process is $5$ minutes and that of the second process is $30\,s$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11}\,s$. The value of $\alpha$ is $..............$

$A$ radioactive sample of half-life $ 10 $ days contains $ 1000x $ nuclei. The number of original nuclei present after $ 5 $ days is: (in $x$)

The half-life period of a radioactive substance is $60 \ days$. The time taken for $\frac{7}{8}$ of its original mass to disintegrate will be $...... \ days$.

$A$ 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:

Which sample contains a greater number of nuclei: a $5.00 \mu Ci$ sample of $^{240}Pu$ (half-life $6560 \ y$) or a $4.45 \mu Ci$ sample of $^{243}Am$ (half-life $7370 \ y$)?