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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.
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Solution
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.
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