Chemical Forums
Specialty Chemistry Forums => Nuclear Chemistry and Radiochemistry Forum => Topic started by: ethylenediamine on November 12, 2006, 12:28:14 AM
-
How do I quantitatively sketch the shape of teh neutrino spectrum for various types of decay? What should I lablel on the axes? Relative number vs. Energy?
a) EC decay of 207-Bi, Q = 2.40 MeV
Since EC decay results in only neutrino and daughter nucleus, I know that the energy is definite. But would I used conservation of momentum? What is the mass of a neutrino?
b) Beta+ decay of 22-Na, Q = 3.86 MeV
How would I do this? I know how the energy spectra for daughter nuclei look, but I don't know how to sketch the one for the neutrino. I think it has the same energy range as that of the daughter nuclei, but how do I find the peak of the curve? Is it the same peak as that of the daughter nucleus? Or would I have to solve the whole Fermi Golden rule equation in variables relating to neutrinos? Then I would differentiate the equation for the peak? *delete me*!!
c) Beta- decay of 14-C, Q = 0.156
Similar to b), but I know that positron and electron decay differ because of the interaction between the electron and daughter nucleus (versus the positron and daughter nucleus interactions).
Remember the question asks for a quantitative answer....
-
a graph of relative number(y-axis) versus energy sounds fine. Your logic seems fine for B and C. For part A if you right down the nuclear equation for it I'll work it through with you.
-
For part A, I think the reaction is as follows:
20783Bi + e- = 20782Pb + neutrino
I would calculate the energy that results:(Mp-MD)*c^2, which is the difference in mass between the parent and daughter.
Then would I use conservation of momentum and energy to find the definite energy of the neutrino? (as in alpha decay, p.180 of Lovleand)
I would guess that the neutrino has energy:(mass of daughter/(mass of daughter +neutrino mass)*Q
But what is the infintesimal mass of the neutrino? Should I just assume that it is massless, so that the energy of the neutrino is exactly Q?
How would I graph relative number on the y-axis? Should they resemble those graphs of 207 of Loveland?
Thanks
-
Assume its massless or go for the 0.3eV your choice. I doubt there will be a noticeable difference.