358 RADIATION OF ENERGY. 



§5. On Planck's Theory of Elementary Quantities op Energy. 



In 1900, Planck, 1 starting with the assumption that the sources of radiant 

 energy are electric oscillators within the atom, proposed the remarkable theory 

 that these oscillators contained heat energy only in multiples of an elementary 

 quantity which he called a quantum and designated by «. Thus, in a 

 volume of gas, some of the molecules would contain an amount of energy equal 

 to le; some, to 2e; others, to 3«, and so on. He assumed that these energy 

 quanta would be distributed among the molecules according to the law of prob- 

 abilities. He further assumed that the magnitude of the quantum varied with 

 the frequency, v, of the oscillator, and indeed was proportional to it, so that we 



given 



would have 



€ 



hv f 



where h is a universal constant. Experiment shows that 



h = 6.548 X 10" 27 ergs X seconds. 



It will be observed that h has the dimensions of energy multiplied by time, and 

 that therefore it has the dimensions of action. Planck called it the Wirkungs- 

 quantum, or the action quantity. It might be called in English the action 



constant. 



The result of making the magnitude of the quantum proportional to the 

 frequency of the elementary oscillator, is that for very high frequencies the 

 quantum becomes very large, and for very low frequencies, very small. But 

 according to the law of probabilities there can only be a few of these very large 

 and very small quanta distributed among the molecules. This means that the 

 energy will be so distributed among the oscillators that those of mean frequencies 

 will have most of it, while those of high or low frequencies will have only a small 

 part of it. This is found by experiment to be actually the case. 



Proceeding on the assumptions stated, Planck found an expression for the 

 mean energy, U, of an oscillator, namely 



(i) 



&, 



e hvlkT __ J > 



where v is the frequency of the oscillator, T is its absolute temperature, and k 

 the universal gas constant . Experiment shows that 



k m 1.346 X 10- 16 ergs/degrees. 



Equation (1) can be contrasted with the expression for the mean kinetic energy 

 of a molecule of a gas given by the kinetic theory of gases: 



(2) 



U = ikT. 



I 



Deutsch. Phys. Gesell., 2, pp. 237-245. 1900: Annalen der Physik, 4, pp. 553-566, 1901 



