Consider a neutron and an electron bound to each other due to gravitational force. Assuming Bohr’s quantization rule for angular momentum to be valid in this case, derive an expression for the energy of the neutron-electron system.

Question

Philoid · Accepted Answer

Applying Bohr’s quantization rule for angular momentum

And due to gravitational force balancing centripetal force.

Using both the equations we get

And

Now substituting these values in

Total energy = K.E + P.E