|San José State University|
& Tornado Alley
|The Proposal by Uhlenbeck and Goudsmit that electrons have spin|
The discovery of the regularities of the radiative emissions of chemical elements is one of the most magnificent accomplishments of the human race. The quantitative development started in the mid-19th century with the joint work of Gustav Kirkhoff and Robert Bunsen. However the discovery that certain minerals could produce distinctive coloration of flames occurred in ancient China.
The claim to fame of Robert Bunsen was the invention of the Bunsen Burner, a device that burned natural gas with an essentially colorless flame. When powdered minerals were dropped into that flame distinctive colors resulted. For example, ordinary table salt produces a golden yellow color. It was then found that other compounds of sodium also produces this color. Therefore the golden yellow color was an indication of the presents of sodium in a mineral. After documenting the colors produces by known elements Kirkhoff and Bunsen went to discover new elements using the flame test.
It was subsequently found that elements did not produce light of a single wavelength but instead a whole spectrum of colors. The wavelengths of the spectra of known elements were measured. The spectrum of sunlight was measured Three amazing discoveries were made. First, he spectrum of sunlight contained the spectra of known elements such as hydrogen. Second, some parts of the spectrum of sunlight did not correspond to the spectra of known elements on Earth. The element helium was discovered in this way. Third, there were some missing wavelengths in the spectra of sunlight that correspond to the spectra of known elements. Kirkhoff identified this phenomenon as the absorption of specific wavelengths of light by a layer of the Sun's atmosphere that is cooler than the layer behind it. Kirkhoff formulated a surprising principle; i.e., that the emission and absorption of a substance are closely related. Now that principle seems obvious because emission and absorption involve the same process of electrons changing their states.
Throughout the rest of the 19th century spectroscopy developed by measuring spectra outside of the visible range of radiation. It also more precision in the measurement of wavelength. By the end of the 19th century the field had mass of quantitative data but no systematic theory to explain it. The step in the direction of the explaining the data was the discovery of a formula that fit part of the spectrum of hydrogen. This was the Balmer series. Balmer was an instructor in a girls high school. He had a hobby of numerology and devoted himself to finding interesting relationships among the numbers for some field such as the dimensions of the pyramids in Egypt. Someone suggested to Balmer that he investigate the wavelength values for the spectrum of hydrogen. Balmer applied his talents and came up with a simple formula that fit the data surprisingly well. That formula was
where λ is wavelength, R is a constant and n is a positive integer. Later others came up with formulas for other parts of the spectrum of hydrogen. All of the formulas were of the general form
where n1 and n2 are positive integers such that n1<n2.
Beginning with Kirkhoff and extending through the rest of the 19th century physicists tried to find a formula for the emission spectrum of a perfect emitter and absorber called a black body. There were some promising candidates proposed for such a formula but success did not come until Max Planck found the right one at the beginning of the 20th century. Planck found that formula by intuition and trial and error. He then applied himself to explaining what he knoew to be the right formula. Planck was trained in the classical tradition and was not prone to making radical modifications for that tradition. Nevertheless he was forced to make a revolutionary formulation; i.e,, that energy changes take place in discrete packets proportional to the frequency of the radiation involved. The constant of proportionality became known as Planck's constant and was denoted as h. This is considered as the beginning of quantum theory. Actually the beginning of quantum theory could be considered the quantization of material mass given by the atomic theory with John Dalton. Next was the discovery of the quantization of charge with Millican's discovery of the electron.
Albert Einstein developed a quantum theory of radiation to explain the photo-electric effect. Radiation is transmitted in packet of energy equal to
where ν is the frequecy of the radiation and h is Planck's constant.
In the early 20th century Neils Bohr began developing a quantum theory of the energy and angular momentum of electrons in an atom. Electrons were presumed to be in states with different energy levels. When an electron changed states a quantum of radiation is emitted. The quantization of the angular momentum of an electron led to a formula for the wavelength of emitted radiation which was the same as the general formula found by Balmer and the others.
The spectra of elements were giving information as to the structure of matter. But the more precise measurement of wavelength was revealing some surprises. Some of the lines in a spectrum were double lines and others were triple. Some single lines became double when observed within a magnet field. There was no immediate explanation for this phenomena or multiple lines in general.
In Bohr's original Quantum Theory the energy of an electron depends only on the principal quantum number of its state. This corresponds to the order number of a circular orbit. The wavelength and frequency of an emitted photon corresponds to the difference in energy of the initial and final state. Further development of the theory led to the notion of elliptical orbits. A second quantum number, called the magnetic quantum number was introduced to account for the shape of the orbit. The energy of the electron then depended upon the magnetic quantum number as well as the principal quantum. A change of state allows for a change in the magnetic quantum number of −1, 0 or +1. Therefore there would be three closely spaced spectral lines corresponding to a particular change in state. But is the tripleness of the spectral line determined by the constraint in the changes to the magnetic quantum or is the constraint derived from the tripleness of the spectral li
It was known since Zeeman's work that the imposition of a magnetic field alters the spectrum by producing three where only one line had been before. Attempts were made to explain this multiplicity of lines by invoking some relativistic effects such as the rotation of elliptical orbits. These efforts were not successful. Then in 1926 two young graduate students in physicists, George E. Uhlenbeck and Samuel A. Goudsmith, published articles noting that if electrons have spin then they would have a magnetic moment that would interact with an external magnetic field. Such interaction would alter the energy of an electron in a particular state. The electron spin could aligned with the magnetic field or anti-aligned. This corresponds to an electron having a spin quantum number of ±½.
If in a transition between states the spin quantum number does not change then there would be no alteration of the wavelength in spectrum compared to the case of with no magnetic field. If the spin quantum number changes from +½ to −½ then the wavelength of a particular line in the spectrum would decrease. A change from −½ to +½ would produce an increase in the wavelength. The increase or decrease in the wavelength would be twice the amount justified by the increase or decrease in energy due to the interaction of the magnetic moment of the electron with the external magnetic field.
(To be continued.)
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