Question

The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is B = `- (Me^4)/(8n^2ε_0^2h^2)`. (m = electron mass). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be

B = `- (Me^4)/(8n^2ε_0^2h^2)` (M = proton mass)

This last expression is not correct because ______.

Options

• n would not be integral.

• Bohr-quantisation applies only to electron

• the frame in which the electron is at rest is not inertial.

• the motion of the proton would not be in circular orbits, even approximately.

Answer 1

The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is B = `- (Me^4)/(8n^2ε_0^2h^2)`. (m = electron mass). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be

B = `- (Me^4)/(8n^2ε_0^2h^2)` (M = proton mass)

This last expression is not correct because the frame in which the electron is at rest is not inertial.

Explanation:

In a hydrogen atom, electrons revolving around a fixed proton nucleus have some centripetal acceleration. Therefore its frame of reference is non-inertial. If the frame of reference, where the electron is at rest, the given expression is not true as it forms the non-inertial frame of reference.