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


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