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## 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 im not sure i think this is wrong, but dont quite understand.