Collisional Broadening

uncertainty principle - pressure broadening - Stark effect

What it shows:
Perturbation by colliding atoms in a high pressure gas result in the broadening of mission and absorption lines. This is clearly seen in the sodium D (589nm and 589.6nm) lines of a high pressure sodium lamp.

The broadening in frequency width is dependant upon the separation of the perturbing particles (Novotny 1973) by

∆ν ∝ r-n

With n=2 the broadening is due to the coulomb field of an ionized atom or electron; this is the linear Stark effect. With n=3 the interaction is between neutral atoms of the same type; this is responsible for the broadening in this demo, and is also important in stellar atmospheres for the broadening of hydrogen lines.

How it works:
The finite duration of the radiation process of electron transition leads to a finite width of line, in accordance with Heisenberg's uncertainty principle. For a high pressure gas, radiating times can be much greater than the interval between atomic collisions, and this perturbation by colliding atoms causes the premature transition and emission of a photon. The decreased lifetime of the state creates an increased uncertainty in photon energy, broadening the emission line.

As the temperature of the gas increases, the collision interval decreases and the broadening becomes more pronounced. Atoms in such a gas cannot be considered as isolated systems and need to be treated statistically, such that due to the perturbations caused by the presence of surrounding atoms, there is no longer a fixed separation between any two energy levels. Likewise, in the process of absorption the energy of an absorption line will be uncertain with a width that is pressure dependant.

The emission structure comes from the central region of the discharge tube where the temperature is hottest. As the lamp heats up (this takes 3-5 minutes), the D lines broaden and merge. At the center of this smudged line (~2 minutes after start-up) a thin absorption line begins to grow. The absorption feature emanates from the cooler gas at the tube's wall; there is a time lag between the emission broadening and the absorption broadening, and the relative widths of these features tells you something about the temperature gradient through the tube.

Setting it up:
The light source 1   is contained within a custom built elliptic housing. 2   Two alternative set-ups are possible, and both have their good and bad points. The spectrum can be projected on a screen using a 5cm focal length convex lens and direct view (Amici) prism. This gives you a nice big spectrum so that the lecturer can point out the various features. Unfortunately you won't be able to resolve the doublet unless you really close down the slit, but then it's too dark to see. The doublet can be resolved using hand held diffraction gratings and looking directly at the slit, but then it's tougher for the lecturer to run through the features.

Comments:
By the time the lamp has heated up (about five minutes), the D doublet has a full width of about 350Å. Superimposed on this is the absorption line with a width of 70Å. Doppler broadening does not offer any contribution to this; with a wall temperature of 1500K, the absorption line would be Doppler broadened by much less than an Ångstrom. Rating ***

References:
1. E. Novotny, Introduction to Stellar Atmospheres and Interiors, (Oxford University Press 1973) pp.206-210
2. J. F. Waymouth, Journal of the IES 6, 131 (1977)
3. E. F. Wyner, "D" Line Radiation in the Afterglow of High Pressure Sodium Arc Discharge, GTE Sylvania Laboratory Report LR85, March 1978

1 Dayton 7V132 400W high pressure sodium lamp LU400/BU with 2V436 ballast transformer. Dayton Electric Co., Chicago, IL 60648
2 Identical to the mercury lamp housing described in Planck's Constant