Since it is bound, the mass of the deuteron is less than the sum of the masses of the neutron and the proton which make it up: (m, + mp) – ma = € = 2.22 MeV/c². Now, a photon with energy of 2.22 MeV has enough energy to break apart a deuteron into a neutron and a proton, both at rest. However, that process will not conserve momentum. A photon that could actually dissociate the deuteron (necessarily conserving both momentum and energy in the process) must have somewhat higher energy than 2.22 MeV. Your goal is to estimate how much. In the end you would like to say that the minimum energy of the required photon is Ey = 2.22 MeV(1 + a), and be able to say what the factor a actually is. There is a slight complication to this calculation which you should ignore for simplicity. The mass of the neutron (939.5 MeV/c²) and that of the proton (938.3 MeV/c²) are not identical. But, for the purposes of this calculation, go ahead and assume that they are the same; That is, assume that the deuteron splits into two exactly equal mass particles (mass m such that 2m – ma = €). Once you have an expression for the factor a you can put in the values e = 2.22 MeV/c² and ma = 1.88 GeV/c². [Hint: Be sure you understand the argument we have discussed for establishing the threshold energy for et - e- pair production.]

The theory of special relativity discusses how space and time are related to objects traveling along a straight line at a constant speed. Simply stated, as an object reaches the speed of light, its mass becomes infinite and it is unable to move faster th…