Calculating Kinetic Energy and Recoil Speed of Nucleus after Electron Capture

[rubertoda]

Hi


I have an atom with nuclear charge Z, mass M and no electrons (a bare nucleus) which captures an electron into its ground state. I am asked to calculate the kinetic energy and the recoil
speed of the nucleus after the electron capture...

I have the Z^2 (-13,6 eV) as usual, as the potential energy for the K-electron...
also i have that momentum is conserved, Mv = -mv, and i ignore relativistic effecta, i.e mv^2/2 is the kinetic energy..but shouldn't there be sthg else involverd? I mean, this sounds to easy

 

[TSny]

During electron capture, what particle is created in the process and ejected from the system? :shy:

 

[rubertoda]

a proton goes to a neutron, at the same time as a neutrino is flewn out..but should i only consider the neutrino energy and equal that to the recoil energy?

 

[TSny]

Nevermind, I see that the captured electron does not go into the nucleus but is captured "into the ground state" of the atom. So, there is no nuclear reaction and no neutrino created. Hmm, seems like an odd question to me. [Maybe replace neutrino with photon?] Sorry for misreading.

 

[rubertoda]

Yes, i thought so to in the beginning, and it is propably true...in that case, i should find out the recoil energy and speed of the nucleus whit mass M and atomic number Z

I start with: the recoil energy = -13.6 Z^2( which is the ground state energy) = Mv^2/2