If Bohr's picture of the atom is correct, explain why the electron behavior of atoms of elements with more than one electron is not well described by the equation (1/wavelength)=R((1/n1^2)-(1/n2^2))

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anonymous · Answer

As far as I know, Bohr's electron model was only ever intended to describe the H atom.  Describing any other atom requires dealing with electron-electron repulsion, and Bohr had no easy way to do that within his semiclassical model.  In any event, before he could develop one, quantum mechanics came along and he embraced that.

As for the more general reason why the wavelength of an emitted or absorbed photon is not described by a function of only the principle quantum numbers, the answer is that the effective potential in which the electron moves has a component due to its angular momentum.  Roughly speaking, you have a centrifugal force opposing the electrostatic attraction, and that means the radial part of the electrons orbit will not be the same for all values of its angular momentum.  Hence, at the least, a formula for the energy levels of an electron in the atom should depend on n *and* l, and they do in multi-electron atoms. That they don't in hydrogen is an "accidental" degeneracy that arises from a non-obvious constant of the motion (the Lenz vector) which would NOT be preserved in a multi-electron atom.

anonymous · Answer

Thank you