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. 

Consider a radioactive nucleus $A$ which decays to a stable nucleus $C$ through the following sequence : $A \to B \to C$ Here $B$ is an intermediate nuclei which is also radioactive. Considering that there are $N_0$, atoms of $A$ initially, plot the graph showing the variation of number of atoms of $A$ and $B$ versus time. 

An archaeologist analyses the wood in a prehistoric structure and finds that ${C^{14}}$ (Half life $= 5700\, years$) to ${C^{12}} $ is only one- fourth of that found in the cells buried plants. The age of the wood is about ……..$years$

The half life of a radioactive sample undergoing $\alpha$ – decay is $1.4 \times 10^{17}$ s. If the number of nuclei in the sample is $2.0 \times 10^{21}$, the activity of the sample is nearly

In the uranium radioactive series, the initial nucleus is $_{92}{U^{238}}$ and the final nucleus is $_{82}P{b^{206}}$. When the uranium nucleus decays to lead, the number of $\alpha – $ particles emitted will be