The half-life of a radioactive substance is $20\, min$. The approximate time interval $\left(t_{2}-t_{1}\right)$ between the time $t_{2},$ when $\frac{2}{3}$ of it has decayed and time $t_{1},$ when $\frac{1}{3}$ of it had decayed is (in $min$)

The half-life period of a radio-active element $X$ is same as the mean life time of another radio-active element $Y$ Initially they have the same number of atoms. Then

For a certain radioactive process the graph between $In\, {R}$ and ${t}\,({sec})$ is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately $….\,{sec}.$

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. 

The fossil bone has a ${}^{14}C:{}^{12}C$ ratio, which is $\left[ {\frac{1}{{16}}} \right]$ of that in a living animal bone. If the halflife of ${}^{14}C$ is $5730\, years$, then the age of the fossil bone is ……….$years$