The Bohr Atom: A guide by Bruce Cameron Reed

Author:Bruce Cameron Reed
Language: eng
Format: mobi, epub
ISBN: 9780750336116
Publisher: IOP Publishing
Published: 2020-10-30T16:00:00+00:00

Now imagine that the electron transits down by one orbit, to orbit n − 1. From equation (2.14), the frequency of the emitted photon, , will be (μ = me)

which reduces to

Note the notational nuance here: the ‘quantal’ frequency of the photon has been adorned with the superscript ‘quant’, a reminder that it is a very different type of frequency than the mechanical one.

Now suppose that n ≫ 1. The square bracket in equation (2.21) reduces to ~2/n3, leaving

This result is identical to that for the mechanical frequency fn. It occurred to Bohr that if n is large, then the atom will become increasingly ‘macroscopic’ in size, where one might expect classical physics to prevail. The calculation supports this intuition in that it tells us that for large values of n, the frequency of the photon emitted in the n n − 1 transition will be essentially identical to the classical ‘mechanical’ orbital frequency of the electron in its initial (or final) orbit. This identity comprised what Bohr saw as a ‘correspondence’ between classical electrodynamics and his new quantum atomic dynamics. In subsequent attempts to elaborate the quantal theory to accommodate multi-electron atoms and molecules, and later during the development of formal quantum mechanics during the 1920s, this Correspondence Principle became a touchstone for Bohr and his collaborators. There is no formal mathematical definition of the Correspondence Principle; rather, it is expressed qualitatively with statements along the lines of ‘The predictions of quantum mechanics should concur with those of classical theory in domains in which the latter are known to be valid, typically situations involving high quantum numbers where the effects of quantization become less and less important’. For more advanced students, some applications of the Correspondence Principle can be found in Crawford (1989).

Continuing with our tour through Paper I, angular momentum makes its first appearance on page 15 (still within section 3), along with the realization that the theory could be developed based on the assumption that ‘ … the angular momentum of the electron round the nucleus … is equal to an entire multiple of a universal value …’, the universal value being h/2π. Bohr generously gives Nicholson credit for pointing out the possible importance of angular momentum in atomic systems.

Section 4 of the paper points out that the theory can explain Kirchhoff’s laws by imagining that an atom can absorb energy from the outside, causing an electron to raise its energy level and thus explain why absorption spectra are the reverse of emission spectra; this section also offers further reflections on the mechanical aspects of atomic systems, and suggests that the emission/absorption theory is somewhat akin to Einstein’s treatment of the photoelectric effect.

In his last section, Bohr deals briefly with treating multi-electron atoms as comprising electrons distributed in rings orbiting the nucleus, but comes to the conclusion that there is no convincing way to explain line spectra on this basis. At the very end of the paper, he reiterates that angular momentum has assumed a primary role,

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