Thomas A. Lehman' Universitk Nationole du Zaire
I
The Planck Radiation l a w the Efficiency of a Light
A
hallmark of chemical education is the considerable attention now given to certain concepts of modern physics, especially quantum theory. The infusion into the curriculum of these ideas and equations almost necessarily entails a reduction in the time devoted to traditional aspects of chemistry. The instructor who wishes to open the general chemistry course with a few lectures on quantum theory can use immediately the experiment described below, for it will both compliment the lectures and require that the students learn to use the analytical balance, as they construct a graph and weigh several sections of it. Thus, time can be devoted to a theoretical approach to chemistry without reducing the number of laboratory hours spent on conventional techniques. The experiment is based on the Planck radiation law, and can be computerized or adapted for use at other levels of instruction. The law has several applications Reprints may be requested from B. R. Willeford, Bucknell University, Levisburg, Pennsylvania 17837. Other correspondence may be sent to the author in Zaire. The radiant energy accounts for only about 7.5% of the total electrical energy used by the bulb. The remainder is condueled away (1). Strictly speaking, all materials emit light s t all temperatures, as can easily be seen from the Planck equation. As the temper* ture increases, the point .of maximum intensity shifts toward shorter wmelengths. The light emitted a t temperatures of no more than a few hundred degrees is usually ignored because of its low intensity. For discussions of blackbody radiation and derivations of the Planek equation, see references (8-4).
832
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Journal of Chemical Education
Bulb
of interest to chemists. These matters will be treated briefly in the Discussion. Introduction
It is sometimes said that an ordinary light bulb is not very efficient-that much of the electrical energy goes instead into heat. This experimcnt uses the Planck radiation equation to determine the efficiency of such a bulb, expressed as the ratio of visible light energy to total emitted energy.2 This ratio defines eficiency for this experiment. Description of Experiment
Theory. A blackbody is one that absorbs all of the light that falls on it. The light energy gained by absorption increases the temperature, which in turn increases the emission of light by the blackbody. The energy spent in emission may be provided in other ways than by light absorption. In the incandescent bulb, electrical energy is put into the filament, which, because of its resistance to an electrical current, becomes hot and emits light.3 The filament gives off energy over a wavelength range that is much wider than the visible region of the spectrum, and is continuous, i.e., there is light at every wavelength in the range. I n doing so, it emits as a blackbody, to a good approximation, and its behavior is given by the Planck radiation e q ~ a t i o n ,which ~ gives the energy density ph as a function of wavdcngth X and absolute temperature T
Here, h is Planck's constant (4.1355 X lo-'$ eV.sec) and c is the speed of electromagnetic radiation (2.9979 X 10" pmlsec). The Boltzmann constant, k, is the constant of proportionality between temperature and energy; its value is 0.8617 X lo-' eV/K. Using the micrometer (pm) as the unit of length, the precise meaning of p, is: the amount of energy per cubic micrometer contributed by radiation of wavelength X '/z pm in any cubic micrometer of space located between any two points of the heated filament. The units of ph are eV/pm4, i.e., eV per unit of wavelength and per unit of volume. Calculation of Eficiency. The radiation equation is used t o calculate the energy density as a function of wavelength at enough points so as to define the cuwe between 0.3 and 4.0 pm. This range includes almost all of the energy emitted at 3000I
