Very Basic Nuclear Reaction Q Value Problem

Hello,

I looked around before and could not find an answer to this question.

So given the reaction

neutron + X -> Y + gamma

and we assume that both initial particles are at rest.

Then using momentum balance we can find that the energy of the gamma is:

Egamma = -m_Y*c^2 + sqrt( (m_Y*c^2)^2 + 2Q*m_y*c^2).

Here is what I don't get. The question says to assume that m_Y*c^2 >> Q. Using the binomial theorem and rearranging the above you get that in the limit, E_gamma -> Q. Why does the energy of the gamma approach Q? I originally thought that the energy of the gamma would approach 0 since the increasing rest mass of Y would cause more energy to be needed as binding energy in Y, thus leaving less energy for the gamma.

Please help... ;)

Thanks.
 
How do you define Q? As an excess energy left after you're done assembling Y from neutron and X? This energy is divided into kinetic energy of Y and energy of the photon. If Y is very heavy compared with Q, it needs very little energy to balance the momentum of the massless photon.
 

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