Which sample contains 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 $7370\, y$)

Deuteron is a bound state of a neutron and a proton with a binding energy $B = 2.2\, MeV$. A $\gamma $ -ray of energy $E$ is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the $n$ and $p$ move in the direction of the incident $\gamma $ -ray. If $E = B$, show that this cannot happen. Hence calculate how much bigger than $B$ must $E$ be for such a process to happen. 

Activity of a radioactive sample decreases to $(1/3)^{rd}$ of its original value in $3\, days$. Then, in $9\, days$ its activity will become

A radioactive material decays by simultaneous emission of two particles with respective half lives $1620$ and $810$ years. The time (in years) after which one- fourth of the material remains is

Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is

$\mathop {^{38}S}\limits_{sulpher} \xrightarrow[{ - 2.48\,h}]{{half\,year}}\mathop {^{38}Cl}\limits_{chloride} \xrightarrow[{ - 0.62\,h}]{{half\,year}}\mathop {^{38}Ar}\limits_{Argon} $ 

Assume that we start with $1000$ $^{38}S$ nuclei at time $t = 0$. The number of $^{38} Cl$ is of count zero at $ t=0$ an will again be zero at $t = \infty $. At what value of $t,$ would the number of counts be a maximum ?

Certain radio-active substance reduces to $25\%$ of its value in $16$ days. Its half-life is ........ $days$