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प्रश्न
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.
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उत्तर
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`.
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