Classical mechanics atomic spectra

The hydrogen atom, containing a single electron, has played a major role in the development of models of electronic structure. In 1913 Niels Bohr (1885-1962), a Danish physicist, offered a theoretical explanation of the atomic spectrum of hydrogen. His model was based largely on classical mechanics. In 1922 this model earned him the Nobel Prize in physics. By that time, Bohr had become director of the Institute of Theoretical Physics at Copenhagen. There he helped develop the new discipline of quantum mechanics, used by other scientists to construct a more sophisticated model for the hydrogen atom. 

We have introduced you to the concepts and methods of quantum mechanics this branch of physics was developed to explain the behavior of matter on the nanometer length scale. The results of a number of key experiments demanded the creation of a new physical theory classical mechanics and electrodynamics failed completely to account for these new observations. The pivotal experiments and observations included the spectrum and temperature dependence of blackbody radiation, the very existence of stable atoms and their discrete line spectra, the... 

The line of thought followed so far may be summarized as follows. Classical mechanics, on the basis of the picture of the electron revolving round the nucleus, certainly enables us to deduce formula) for the connexion between orbital radius, frequency of revolution, and energy, but it is incapable of explaining the spectrum emitted by the atom. Tor the latter purpose we have, following Bohr, to introduce a new hypothesis, viz. that the atom only possesses certain definite energy levels Bn = and it is the business of the new mechanics to... 

It remained for Bohr (1913) to break with classical mechanics and apply the quantum concept of Planck to atoms and atomic spectra. The model proposed by Bohr and the equation he developed for the spectrum of atomic hydrogen were based on a set of new postulates, including the following ... 

Despite the fact that we treated vibrational and rotational spectroscopy first, the astute student will recognize that one of the mysteries of classical mechanics involved electronic spectroscopy. The inability to explain the (electronic) spectrum of the hydrogen atom was a major reason for the development of quantum mechanics. Yet, we have put off a detailed discussion of it until after considering rotational and vibrational spectra. 

A diatomic molecule approximates the model just discussed such that the mass of one atom is much larger than the other atom such as hydrogen bromide. In infrared spectroscopy, the absorbed infrared radiation results in transitions in both the vibrational and rotational states of a molecule. Considering only the vibrational transitions, what would an infrared spectrum of hydrogen bromide look like based on the classical result According to classical mechanics, would infrared spectroscopy be a useful tool in chemistry ... 

The continuous spectrum is thus characterized by a short-wavelength limit and an intensity distribution. Experiments on other target materials have shown that these characteristics are independent of the target material although the integrated intensity increases with atomic number. (See Equation 1-3.) The continuous spectrum, therefore, results generally from the interaction of electrons with matter. Attempts (none completely successful) have been made to treat this interaction theoretically by both classical and quantum mechanics. 

Tn the Rohr model of the hydrogen atom, the proton is a massive positive point charge about which the electron moves. By placing quantum mechanical conditions upon an otherwise classical planetary motion of the electron, Bohr explained the lines observed in optical spectra as transitions between discrete quantum mechanical energy states. Except for hvperfine splitting, which is a minute decomposition of spectrum lines into a group of closely spaced lines, the proton plays a passive role in the mechanics of the hydrogen atom, It simply provides the attractive central force field for the electron,... 

In 1913 Bohr amalgamated classical and quantum mechanics in explaining the observation of not only the Balmer series but also the Lyman, Paschen, Brackett, Pfund, etc., series in the hydrogen atom emission spectrum, illustrated in Figure 1.1. Bohr assumed empirically that the electron can move only in specific circular orbits around the nucleus and that the angular momentum pe for an angle of rotation 9 is given by... 

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