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’:

Estimate the value of (e’/e) given that the binding energy of a deuteron is 2.2 MeV.

The value of

Given

The force between neutron and proton is given by, the binding energy of the deuteron is.

Formula used

Binding Energy of H-atom orbital derived from Schrödinger equation. The Schrödinger equation states the wave function of a quantum mechanical system by the use of linear partial differential equation.

For H-atom

For Deuteron

where

E and E’ are the binding energy for H-atom and Deuteron respectively, m is the mass of proton, m’ is the reduced mass of proton and neutron e’ is the effective charge of deuteron and e is the charge of H-atom, h is the planks constant =

Explanation

The binding energy of the H-atom is

The binding energy of H-atom is known as

Hence,

The binding energy of the deuteron is

The binding energy of deuteron is known as

Hence,

To find the value of reduced mass m’ in term of m we use the formula

where

is the mass of proton and neutron respectively.

So the binding energy of deuteron is

Equating both the binding energy in a ratio we get;

Solving the equation in terms of , the result is

Therefore, the value of