Atomic Spectra and Quantum Numbers

Abstract

From the viewpoint of a planetary model of the atom, the discrete emission spectrum of hydrogen (and the other elements) made no sense. After all, like planets orbiting the sun, electrons should be able to orbit an atomic nucleus at any conceivable frequency. So according to the Maxwell’s theory of electrodynamics, they should be capable of emitting every conceivable color of light. But atomic gases typically emit (and absorb) only particular colors. Moreover, orbiting electrons should continually emit radiation—and hence lose energy—spiraling into the atomic nucleus. The atom should thus be unstable.

In order to address these seemingly fatal flaws of the planetary model, Bohr made two novel postulates. First, he proposed that electrons can reside in so-called stationary states.When in one of these peculiar states, either the electron is not moving (hence, it is “stationary”), or the classical theory of radiation simply does not apply. How such a scenario might arise Bohr could only surmise. Second, he proposed that when an electron makes a transition between two stationary states, it emits a single photon—Einstein’s proposed quantum of light—whose frequency (as it were) is determined strictly by the energy difference between the initial and final stationary states. Bohr’s two postulates, when appended to the planetary model, were able to account (at least nominally) for the empirical formula developed by Balmer and Rydberg to describe the emission spectrum of hydrogen. In the reading selection that follows, which is a continuation of his 1922 Nobel lecture, Bohr explains how his model was expanded so as to account for the emission spectra of atoms having more complex electronic structures. In so doing, he introduces the reader to the concept of quantum numbers.

The stationary states compose a more complex manifold, in which, according to these formal methods, each state is characterized by several whole numbers, the so-called quantum numbers.

—Niels Bohr