Atomic Spectroscopy (Emission Spectroscopy)

    Perhaps the most important experiments for the development of quantum theory were those using atomic spectroscopy. There are two general types of atomic spectroscopy, absorption and emission spectroscopy. In emission spectroscopy a sample of atoms is “excited,” usually with an electrical discharge such as a spark. This has the effect of exciting the atoms, not just to the first excited state, but to a variety of excited states. In general, however, these states have finite lifetimes. When they decay to lower states, not just the ground state, they do so by emitting light. (Whether visible or not, physicists generally refer to electromagnetic radiation as
“light.”) Because the energy levels are uniquely quantized for each atom, the energy of the emitted light is quantized and hence, in accord with Equation 1.3, the wavelengths that are emitted are unique. Emission spectroscopy is routinely used for identification and trace analysis. In the early days of spectroscopy, the latter part of the nineteenth century and the beginning of the twentieth century, the detector in common use (aside from the human eye) was a photographic plate. Using prisms or diffraction gratings, the light in an emission spectroscopy experiment was dispersed into its constituent wavelengths and focused on a photographic plate. Because only certain discrete wavelengths were emitted most of the plate was dark, that is, not exposed. The portion that was exposed exhibited lines at the discrete wavelengths emitted by the atoms. These atomic spectra were thus known as “line spectra” and the transitions are known, even today, as lines.
Figure 1.3 shows a schematic diagram of a photographic plate of an emission spectrum of atomic hydrogen. Never mind that hydrogen occurs naturally as

Fig. 1.3 Schematic diagram of a photographic plate of the emission spectrum of atomic
hydrogen in the visible region of the electromagnetic spectrum. Shown are the lines
of the Balmer series
diatomic molecules. When an electrical discharge occurs, most of the molecules dissociate and become atoms, so the observed spectrum is predominantly that of atomic hydrogen. The first lines of atomic hydrogen to be discovered were those of the Balmer series, so named because in 1885 a Swiss school teacher, J. J. Balmer,
without any physical explanation, set forth a formula that accurately predicted the observed wavelengths of the known lines of atomic hydrogen.
    The wavelengths of these Balmer lines had been known for many years, but it was Balmer who first related them through his now-famous formula. There are many other lines in the spectrum of atomic hydrogen, but the lines of the Balmer series were discovered first because the strongest of these lines lie in the visible region of
the spectrum. The Balmer series actually terminates in the near-ultraviolet region of the spectrum at a wavelength of about 365 nm (see Problem 3). Because Balmer was unaware of the origination of these lines he designated them Hα, Hβ and so on, meaning the first hydrogen line, the second line, and so on. The lines of series that were discovered later employ a similar designation, but using the first letter of the discoverer’s name. For example, the first line of the Lyman series is Lα. The wavelengths of the Balmer lines λB are given by the relation

where n is an integer that is greater than 2. Thus, for example, the wavelength of Hα is 656.2 nm. Equation 1.7 can, however, be put in a more convenient form for later use by writing the inverse of the wavelength:

where RH is called the Rydberg constant because Johannes Rydbergwas instrumental in developing a generalized version of Equation 1.8 that predicted the wavelength λnm between any two states, m and n, of hydrogen. In this generalized formula the 2^2 was replaced by the square of another integer. Thus,

 From Equation 1.7 and the known Balmer wavelengths, RH ≈ 1.097 m−1. While the Balmer formula was deduced on purely empirical grounds it was, as we shall see, crucial to the development of the Bohr theory of hydrogen.
    There is a very useful relation between the wavelength of light λ and the energy E of a photon of that wavelength. This relation is easily obtained from Equation 1.3 using convenient units, nm and eV. We have

For example, according to this simple formula, the energy per photon of red light of wavelength 620 nm is 2eV. On the other hand, photons having energy of 5eV correspond to a wavelength of 248 nm.
    Absorption Spectroscopy In absorption spectroscopy a continuous source of light such as light from an incandescent bulb (blackbody radiation) irradiates an atomic sample. The light passing through the sample is detected. Again a photographic plate may be used as the detector. In this case the background is the continuous bright incident light, but there are “holes” in the continuum due to absorption at specific wavelengths by the atomic sample. This might be thought of as a Frank–Hertz experimentwith photons. One of the earliest such experiments was performed in 1824 by Fraunhofer. He dispersed the light from the sun. His continuous source was the solar interior and the atomic sample was the solar atmosphere. There are also molecules in the solar atmosphere, but let us concentrate on the atomic constituents. Fraunhofer observed an abundance of lines which he labeled alphabetically from the red end of the spectrum. Because the solar atmosphere contains hydrogen it would be surprising if lines of the Balmer series were not present. Indeed, C and F are Hα and Hβ , respectively. Interestingly, the fourth line from the red end, a strong “hole” in the yellow portion of the spectrum, was, of course, labeled D. We now know this line (actually a pair of lines)
to be the result of absorptions by atomic sodium. Observation of the “D-line” is a favorite test for the presence of sodium in elementary chemistry. In that test, the heat from the flame from the Bunsen burner excites sodium atoms to the first excited state from which they decay, emitting yellow light, the D-line.

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reference : C.E. Burkhardt, J.J. Leventhal, Foundations of Quantum Physics, 1
DOI: 10.1007/978-0-387-77652-1 1, C Springer Science+Business Media, LLC 2008


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