How Do You Calculate Particle Density in a Star Using Electron Energy?

[tanaygupta2000]

Homework Statement

At what particle density does a completely degenerate electron gas in a star have enough kinetic energy per particle to permit the reaction
p + e + 0.8 MeV -----> n
where p, e and n are proton, electron and neutron respectively. What is the minimum density of the neutron star?

Relevant Equations

The relation between energy E and electron density n is given by :
E = (h^2)/8m (3n/π)^2/3

I am confused whether for electron I have to use rest mass energy (m_oc² + 0.8 MeV) or just 0.8 Mev for calculating E.
Also how do I find minimum density of a neutron star using above data ? Please help !

 

[tanaygupta2000]

How do I solve such a problem ?