ROBERT C. PLUMB
chemical principles exemplified
Light Bulbs Filled with Krypton Gas Illustrating principles of kinetic theory of gases
The "birthdate" of the light bulh is considered to be October 21, 1879, when Edison, after more than a year of intensive experimentation succeeded in creating a hulb which burned for 40 hr. Since then the light bulh has evolved to a commonplace item-mass produced, with a tungsten filament and filled with inert argon gas-which will burn for 750 hr. In recent years Duro-Test Corporation has introduced a new line of light bulbs using krypton gas, which have a life expectancy of 3000 hours, and several other advantages as well. A physical chemistry teacher or student can learn a great deal about the kinetic theory of gases by becoming acquainted with the effects of replacing argon with krypton in a light bulh. The atomic weights of argon and krypton are 39.95 and 83.80 g/mole, respectively. As a consequence, krypton atoms move more slowly than argon atoms at a particular temperature.
The effective diameter of the argon atom is somewhat less than that of the krypton atom. As a consequence, the mean free path, A, of argon atoms in the gas phase is longer than that of krypton atoms at the same temperature and pressure. The mean free path varies inversely with the cylindrical volume swept out by a molecule and this volume varies as the square of the radius.
Estimates of the relative radii of the two atoms varv from 1.05 to 1.15 depending on the phenomenon and theoretical model heine considered. Moreover the effective radius varies with temperature. In this discussion we will not try to specify by how much the mean free path in argon is greater than that in krypton. The rate a t which thermal energy is transported from the hot filament to the glass wall will he substantially greater in the argon atmosphere than in the krypton atmosphere because the thermal conductivitv. r . increases directlv with The both the average speed and wit the mean free observed thermal conductivities of the two eases are in the ratio & k - 44.22 X 10-V(cal/cm2sec T) - 2356 X 10-"cal/cmZ sec 'C) = 1.88 K,, Three practical advantages of the krypton filled hulh are apparent. 1) Operating a filament in a hulh with krypton will result in lower
heat losses than in a bulb with argon, 388 / Journal of Chemical Education
hulh with krypton could be made proportionally smaller than a hulb filled with argon. 3) The filament of a krypton filled hulh could he run at a higher temperature than the filament of an argon hulh, hence giving a higher color temperature and a whiter light. 2) A
The manufacturers, in optimizing these three variables, have produced a product which gives savings and - in power . size a i d increased whiteness. Krypton provides another advantage over argon; the filament does not burn out as quickly and the glass does not darken as rapidly. The hulh life is increased by a factor of approximately three. The prolonging of life results from kinetic-molecular characteristics of krypton and argon, as follows. Tungsten tends to evaporate from the hot filament and condense on the glass surface. (The process is complicated by the effects of traces of oxygen and water which produce tunesten oxides which are more volatile than tunwten: . these complications do not substantially alter the analysis which will follow of the molecular Drocesses occurrine - when tungsten suhlimes into an atmosphere of either krypton or areon.) Consider the elastic head-on collision of two oarticles moving along a line.
The velocities after the collision, V', are related to the masses m l and mp and the velocities before the collision, V, by the equations
If # 2 is a krypton or argon atom, and is assumed to he essentially a t rest with respect to #1, a tungsten atom, approaching it, the velocity of the tungsten atom after the collision will he
As an observer of billiards realizes, if m l = ma, V' will be zero for all values of V1. However, the atoms of tungsten have a mass greater than that of krypton or argon atoms. The atomic weight of tungsten is 183.85. Using the atomic weights of the three types of atoms one finds for tungsten striking argon: V,'/V, for tungsten striking krypton:V,'/V,
= =
0.64 037
The more massive krypton is more effective in slowing down tungsten atoms than is argon. One such head-on collision with a krypton atom will remove 86% of the kinetic energy of a tungsten atom. Afterwards the tungsten atom, moving slowly, has a much greater chance of colliding with
the filament surface again and being re-hound to the solid. The gas acts like a "blanket" decreasing the rate of diffusion and hence reducing the rate of evaporation of the fila-
ment. Krypton is more effective for this purpose than is argon; filament8 do not burn out as quickly and the glass stays free of tungsten deposits longer.
Volume 52, Number 6, June 1975 / 389
