Proportion of energy gained by decay products

[Punch]

What is the proportion of energy gained by the decay products when a nuclei undergoes alpha decay?

 

[daveb]

It depends upon the decay energy. Energy is conserved, but so is momentum, so the parent nucleus experiences some recoil. The more massive the parent nuclues, the less the recoil (relative to the momentum of he alpha, that is).

 

[Punch]

Hello! Thank you for your reply. Sorry, you may have misunderstood my question.

I understand that the amount of energy gained by the decay products depends on how massive the parent nucleus is.

However, my question is: Assuming that we a total of 10MeV to be gained by decay products, 235-Uranium and 4-Helium as KE, how do we determine the proportion of the 10MeV gained by each decay product.

 

[mfb]

Use the conservation of energy and momentum: In the rest frame of the plutonium nucleus, both U and alpha will get the same momentum magnitude p. Their kinetic energies are then given by E_{uranium}=\frac{p^2}{2\cdot 235amu} and E_{alpha}=\frac{p^2}{2\cdot 4amu}. The sum has to be 10 MeV, solve this for p and plug in the equations again to get the energies for both decay products. You can use the true masses instead of the 235amu and 4amu approximations here if you like, but it will not change to result much.