Deuteron is a bound state of a neutron and a proton with a binding energy
. A 
-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 
-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 E should be bigger by B, by 
Given
The binding energy of
, the binding energy of the nucleus is B, the energy of the gamma ray is E, therefore, to find the energy difference we will use the momentum conservation theorem.
Formula used
Conservation of momentum: Find the conservation of momentum before and after collision both in terms of kinetic energy and Binding and wave energy.
where
The kinetic energy and momentum of proton and neutron as 
respectively, the energy of gamma radiation is E and binding is given by B.
Explanation
As the question says the binding energy of
, a gamma radiation is bombarded on the deuteron to break it open into nucleons; the momentum should be conserved in such a way that after collision the neutron and proton should move in the same direction of which the gamma ray had hit the deuteron initially.
The conservation of momentum is written as
_________________(A)
Now the sum of the kinetic energy of both neutron and proton is equal to the energy produced by gamma ray subtracted by Binding energy of deuteron.
With E = B, placing E in place of B we get
This means that the sum of the value of the momentum is also equal to zero
Now the question says that if E = B, then the deuteron won’t crack, so let us check what happens if the value of E is bigger than B
Let us take the value of 
, now the value of X is X<<B
Therefore, to the excess energy required we solve the equation of conservation of momentum
Solving and simplifying the solution we get two roots,
taking the value of 
, we find the real value of the energy required for the nucleons to travel the same path as that of the incidence gamma ray
Therefore, the E should be bigger by B, by 