A 238-U nucleus emits a 4.196MeV alpha particle. Calculate the disintegration energy Q for this process, taking the recoil energy of the residual 234-Th nucleus into account.
The Attempt at a Solution
I tried to answer this question by finding the difference in mass energy between the products and reactants. The mass of the products is 234.04363u + 4.00260u. The mass of the reactant is 238.05079u. The difference in mass energy between the reactants and products is 4.247613 MeV. I found this by taking
(238.05079u)(931.494013 MeV/u) - (234.04363u + 4.00260u)(931.494013 MeV/u)
= 4.247613 MeV.
Doesn't this have to be the disintegration energy by definition? The answer key I have requires that you equate the momentum of the reactants and products, then write them in terms of kinetic energy. It also says that Q = KE(thorium) + KE(alpha particle) at the end of the reaction. The answer it gets is slightly different than mine (it gets 4.268 MeV).
Is there some reason why you can't just find the difference in mass energy the way I did? Given the fact that the answer key introduces momentum, I'm guessing I have to use it to get the answer. But I'm still scratching my head re. why my way is slightly off.