- #1
Matt atkinson
- 116
- 1
Homework Statement
Consider;
[tex]p+p \rightarrow d + e^+ + \nu_e[/tex]
Assume the binding energy of deuteron is 2.2MeV, calculate the maximum energy that the positron can have.
Homework Equations
[itex]m_p=938.28MeV/c^2[/itex]
[itex]m_n=939.566MeV/c^2[/itex]
[itex]m_d=1875.6MeV/c^2[/itex]
The Attempt at a Solution
Assuming the neutrino was at rest after the colision for maximum positron energy.
So basically two process's go on, the [itex]\beta^+[/itex] decay of one of the protons, then the fusion of the neutron and remaining proton.
[tex] (1) \quad p \rightarrow n + e^+ +\nu_e [/tex]
[tex](2) \quad p+n \rightarrow d [/tex]
The Q value of the decay:
[itex] Q=(m_p)c^2-(m_n)c^2=-1.286MeV [/itex]
this is the minimum energy the proton would need to decay to a neutron?
so the energy i got was;
[tex] T_{e^+}=2.2-1.286=0.914MeV [/tex]
where the 2.2 is the energy released from (2)?
But I am not sure i think this is wrong, but don't quite understand.