# Recoil energy from neutrino question

• Exulus

#### Exulus

Hi guys,

I've been struggling with this problem for a while now and can't seem to get anywhere with it. Roughly speaking:

We are given that an Ar37 atom decays through electron K capture into a Cl37 atom and a neutrino, plus a gamma ray of wavelength 4.2 Angstroms. The binding energy of the K capture is 3KeV and the mass difference between Ar37 and Cl37 is 816KeV. We've been asked to calculate the recoil energy of the Cl37 atom when the neutrino is emitted. We know the answer is 9.6eV but can't seem to get anywhere near it!

So far I've calculated the Q value to be 813KeV through the mass difference minus the binding energy of the captured electron. I've tried using linear momentum conservation knowing that the energy of the neutrino is E = pc. However, I can't even see how to begin.

Can anyone offer any starters? I've tried searching everywhere :( Thanks. I believe these are all the values we need to calculate it, but i am at a loss on what to do!

Last edited:
Hi guys (originally posted in the nuclear forum but since found this one),

I've been struggling with this problem for a while now and can't seem to get anywhere with it. Roughly speaking:

We are given that an Ar37 atom decays through electron K capture into a Cl37 atom and a neutrino, plus a gamma ray of wavelength 4.2 Angstroms. The binding energy of the K capture is 3KeV and the mass difference between Ar37 and Cl37 is 816KeV. We've been asked to calculate the recoil energy of the Cl37 atom when the neutrino is emitted. We know the answer is 9.6eV but can't seem to get anywhere near it!

So far I've calculated the Q value to be 813KeV through the mass difference minus the binding energy of the captured electron. I've tried using linear momentum conservation knowing that the energy of the neutrino is E = pc. However, I can't even see how to begin.

Can anyone offer any starters? I've tried searching everywhere :( Thanks. I believe these are all the values we need to calculate it, but i am at a loss on what to do!

[I realize this should be in a specific form but I'm literally about to go out right now, I will be back later and edit it if nessesary, thanks]

Have you taken the X-ray into account in your momentum conservation calculations?

Just want to say this has been solved now :)

Thanks. This has been solved now! Didn't need to take into account the x-ray emission. It was simply a case of using E = p^2/2m...doh!