MCQ
The binding energy of a H-atom, considering an electron moving around a fixed nuclei $($proton$)$, is $\text{B}=-\frac{\text{me}^4}{8\text{n}^2\in_0^2\text{h}^2}. (m =$ electron mass$).$
If one decides to work in a frame of reference where the electron is at rest, the proton would be moving arround it. By similar arguments, the binding energy would be,
$\text{B}=-\frac{\text{me}^4}{8\text{n}^2\in_0^2\text{h}^2} (M =$ proton mass$)$
This last expression is not correct because:
  • A
    n would not be integral.
  • B
    Bohr$-$quantisation applies only to electron.
  • The frame in which the electron is at rest is not inertial.
  • D
    The motion of the proton would not be in circular orbits, even approximately.

Answer

Correct option: C.
The frame in which the electron is at rest is not inertial.

In a hydrogen atom, electron 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.

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