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