The binding energy of a H-atom, considering an electron moving around a fixed nuclei (proton), is 
(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 
This last expression is not correct because
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In the frame of reference where electron is at rest the given expression cannot be true for binding energy as the frame in which electron is a rest would not be inertial in hydrogen atom electron revolving around a fixed proton nucleus has some centripetal acceleration.
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