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The Stark Effect

Half way through my undergrad degree in physics, Prof Ostlie looked up from the Quantum Physics course role and, as if noticing my name for the first time, asked, "Mr. Stark, did you know your name was famous in physics? There is an effect with your name on it." I'd never heard of it before and now it was too late to change majors so I thought I'd better find out what it was. This page is a short description of the spectroscopic phenomena observed by Johannes Stark in 1913, the stark effect. Yes, Dr. Stark's work is the only reason this site's name is any good, otherwise I'd have to make my own physics discovery to put my name on.

What is the Stark Effect

The Stark Effect is shown here in the splitting and shifting of spectral lines in hydrogen under the influence of an external electric field.

The stark effect is the shifting and splitting (reduction of degeneracy) of spectral lines in atomic or molecular species under the influence of an externally applied electric field. It is sometimes considered the electric analog to the reduction of degeneracy in atomic and molecular species due to an externally applied magnetic field, the Zeeman effect. I'm not fond of that characterization since the two phenomena are quite different, but it is a reasonable viewpoint.

There are actually two types of stark effect: the linear stark effect and the quadratic version of the stark effect. As expected, the linear stark effect is linearly dependant on the applied electric field while the quadratic stark effect is smaller in the value of splitting and varies as the square of the applied electric field.

History of the Stark Effect

When Zeeman discovered the effect of magnetic fields on the wavelengths of emitted spectra from an excited gas, the Zeeman effect, it sparked a search for a similar effect due to electric fields. For fifteen years the search failed to show such an effect and as a matter of fact, Woldemar Voigt of Göttingen (known for the discovery of the Voigt effect) showed on a theoretical basis, with some assumptions, that no such effect should be expected.

Experimental failure to find the effect of electric fields on emitted spectra was actually due to a very simple phenomenon. Excitation of atoms to show spectra was usually performed by passing an electric arc through a gas. The gas would be ionized allowing current to flow via motion of the freed electrons and collisions between electrons and ions or electrons and neutral atoms would excite the ions or atoms and then spectra would be visible as the ions or atoms decayed back down from their excited states. The problem is that applying an external electric field to this highly conductive gas simply rearranges the charges such that the electric field within the gas is neutralized and you have no appreciable fraction of the emitting ions or atoms experiencing any electric field at all. Johannes Stark, in 1913, recognized the importance of lowering the conductivity of the luminous gas in order to maintain a strong electric field within the gas. His method for accomplishing this was to examine the spectra emitted by the luminous canal rays behind a perforated cathode. Goldstein discovered these canal rays were discovered by Goldstein and used by Stark to demonstrate the doppler effect. Stark added a second electrode immediately behind the perforated cathode and applied a strong electric field between this new electrode and that cathode. He found that he could maintain several hundred thousand volts per centimeter between them. He also found that the Hydrogen lines emitted by these canal rays were split into polarized components.

Johannes Stark won the Nobel Prize for his demonstration of the Stark Effect.

When Stark aimed his spectroscope at the region between the electrodes from the side, he found the transverse effect where spectral lines were split into symetrically polarized components on the right and left of the original line. Separation between these components varied linearly with electric field strength, the linear Stark effect. If the field is strong enough, you can also see the quadratic Stark effect in which the separation varies with the square of the applied electric field. With a different arrangement of electrodes, Stark also observed the longitudinal effect parallel to the electric field. Each Balmer line was separated into a number of components. That number increased with the serial number of the line so that the red H line is split into the smallest number (9). Observing perpendicular to the field some of the components seen are polarized parallel to the field while others are polarized perpendicular to the field. Observing in a direction parallel to the electric field, those perpendicularly polarized components appear unpolarized, while the parallel polarized components disappear.

Theory of the Stark Effect

The best way to approach the Stark Effect theoretically is by perturbation theory. The idea is that we have the Hamiltonian of the atom or molecule describing the energies and wavefunctions in the absence of an applied electric field and we simply assume that the change in the Hamiltonian, when we apply an external electric field, can be expressed as a smaller "perturbation" on the main Hamiltonian:

Applications of the Stark Effect

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