Question

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 force between neutron and proton in deuteron as given in the form of a Coulomb potential but with an effective charge e′: F = `1/(4πε_0) e^('2)/r` estimate the value of (e’/e) given that the binding energy of a deuteron is 2.2 MeV.

Answer 1

The binding energy in H atom E = `(me^4)/(8ε_0^2h^2)` = 13.6 eV  .....(1)

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 e by e′.

`m^' = M/2 = (1836m)/2 = 918m`

∴ Binding energy = `(918me^')/(8ε_0^2h^2)` = 2.2 MeV  (given)  .....(2)

Diving (2) by (1)

`918(e^'/e)^4 = (2.2  MeV)/(13.6  eV)`

⇒ `e^'/e ≈ 11`.