The deuteron is bound by nuclear forces just as H-atom is made up of p and e bound by electrostatic forces. If we consider the forces between neutron and proton in deuteron as given in the form of a Coulomb force but with an effective charge e': `F=1/(4piepsilon_(0)) (e'^(2))/r^(2)`
estimate the value of `(e'//e)` given that the following binding energy of a deuteron is 2.2MeV.

Explanation

The binding energy is H-atom
`E=(me^(4))/(piepsilon_(0)^(2)h^(2)) =13.6eV" ".........(i)`
if proton and neutron had charge e' each and were governed by the same electrostatic force then in the above equation we would need to replace electronic mass m by the reduced mass m' of proton-neutron and the electronic charge by e'
`m'(MxxN)/(M+N) =(M)/(2)`
`=(1836 m)/(2) =918m`
Here M represents mass of a neutron`//`proton
Binding energy `=(918m(e)^(4))/(8epsilon_(0)^(2)h^(2)) =2.2MeV`
Dividing Eqs. (ii) and (i) we get
`918((e)/(e))^(4) =(2.2 MeV)/(13.6 eV) =(22 xx 10^(6))/(13.6)`
`((e)/(e))^(4) =(2.2xx 10^(6))/(13.6xx 918) =176.21`
`(e)/(e) =(17621)^(1//4) =3.64.`