[ethylenediamine]

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....

[Mitch]

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.

[ethylenediamine]

For part A, I think the reaction is as follows:

²⁰⁷₈₃Bi + e^- = ²⁰⁷₈₂Pb + neutrino

I would calculate the energy that results:(M_p-M_D)*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

[Mitch]

Assume its massless or go for the 0.3eV your choice. I doubt there will be a noticeable difference.