(Q-6) Expansion of the Bohr Model

The Sodium Atom

    Following Bohr's early success with his model of the atom, he tried to extend it beyond hydrogen, in a joint effort with an older associate, the German theorist Arnold Sommerfeld. They noted that atoms like sodium were somewhat like hydrogen, since their chemical activities implied that just a single electron was involved. That suggested a single active electron orbiting far from the nucleus, while the rest of the electrons clustered up closer to the nucleus.

    The observed energy levels of sodium have some similarities to those hydrogen (shown at the right edge of the drawing above, for comparison), although each level is now split into a whole family--the n=4 level, for instance, splits into (4s, 4p, 4d,4f) [the letters have historical reasons, of no interest here]. Bohr and Sommerfeld thought these represent orbits with different ellipticity, and therefore, different angular momenta. Presumably, this shifts the energies of the levels--though no one could calculate those shifts. The lines connecting energy levels represent "allowed" transitions, which can emit a photon. Obviously, only some of the many possible transitions occur in nature

Magnetism and Electron Spin

    For instance, lithium, sodium, potassium--also rubidium and cesium--all had similar chemical behavior, consistent with a single active electron; the rest of the electrons formed in a tight spherical cluster centered on the nucleus. Such repeating patterns (quite a few exist) were first deduced in the 19th century by the Russian chemist Mendeleev ("Mendeleyev"), who used them to predict the existence of some yet-undiscovered elements.

    The electrons remaining in the tight central "cores" of lithium, sodium, potassium etc. seemed to represent quite stable arrangements. The elements just ahead of them on the list--helium, neon and argon--were "noble gases" which resisted any chemical combination, suggesting that all their electrons were in that core, in a bond so stable that no other atom could break into it.

    What determined the number of electrons in that "core"--and therefore, the number of elements one needed to pass before a new "period" was formed? Lithium was the 3rd element--so its core had 2 electrons. Sodium 11th--meaning 10 electrons in the core, 8 more than lithium, probably as a "second layer" on top of the one of lithium (and so forth). By then the arrangement of energy levels was known from spectra, each with a number of "allowed" states of angular momentum, and the idea was that they formed "shells" in which allowed energy levels were completely filled. The scheme indeed worked, but only after Pauli suggested that each level accommodated exactly two electrons of opposite spins. Among heavier elements, sometimes shells filled in an order different from the one expected (some "outer" ones ahead of "inner" ones), but again, the pattern seemed sensible.

    But only the pattern! One could perhaps classify the ordering of energy levels, but not predict their values. Nor could one predict the intensity of field lines--if an atom was at energy level "A", what were the relative probabilities of it jumping to "B" or to "C"? As one example--why was the transitions involving the double yellow line of sodium so prevalent that its light dominated all other emissions from that atom?

    And if the atom seemed to resemble a miniature planetary system, why did the frequencies of the photons it emitted seem unrelated to the orbital frequency calculated for such planetary motions? And why the arbitrary rules about angular momenta? The Bohr-Sommerfeld theory seemed to give plenty of hints, but no precise answers.