NCERT Physics Class 12 Exemplar Ch 13 Nuclei Part 4
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23 The deuteron is bound by nuclear forces just as Hatom 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 given that the binding energy of a deuteron is .
Ans:

The binding energy in H atom

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 protonneutron and the electronic charge e by e′ .
∴ Binding energy (given) 2
Diving (2) by (1)
24 Before the neutrino hypothesis, the beta decay process was through to be the transition,
If this was true, show that if the neutron was at rest, the proton and electron would emerge with fixed energies and calculate them. Experimentally, the electron energy was found to have a large range.
Ans:

Before decay, neutron is at rest. Hence,

After decay, from conservation of momentum:
Or
Also,
From conservation of energy:
Since the energy difference between n and p is small, pc will be small, , while pc may be greater than
To first order
This gives the momentum.
Then,