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 $7370\, y$)

A radioactive element has half life period $800$ years. After $6400$ years what amount will remain?

Write the definition of half life of radioactive substance and obtain its relation to decay  constant.

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. 

A freshly prepared sample of a radioisotope of half-life $1386 \ s$ has activity $10^3$ disintegrations per second. Given that In $2=0.693$, 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 ratio activity of an element becomes $\frac{{1}}{{64}} th$ of its original value in $60\, sec$. Then the half life period is ............$sec$