Ncert Exercises & Solutions

The binding energy of a H-atom, considering an electron moving around a fixed nucleus (proton), is,

$B = - \frac{{me}^{4}}{8 n^{2} ε_{0}^{2} h^{2}}$ ($\mathrm{m}=$ 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,

$B = - \frac{{Me}^{4}}{8 n^{2} ε_{0}^{2} h^{2}}$ ($\mathrm{M}=$ proton mass)
This last expression is not correct, because,

1.	$\mathrm{n}$ would not be integral
2.	Bohr-quantisation applies only to electron
3.	The frame in which the electron is at rest is not inertial
4.	The motion of the proton would not be in circular orbits, even approximately.

(c) Hint: The mass of an electron is negligible as compared to that of a proton.

When one decides to work in a frame of reference where the electron is at rest, given expression is not true as it forms the non-inertial frame of reference.

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1.	\(\mathrm{n}\) would not be integral
2.	Bohr-quantisation applies only to electron
3.	The frame in which the electron is at rest is not inertial
4.	The motion of the proton would not be in circular orbits, even approximately.