September 30, 1921] 



SCIENCE 



289 



view briefly some of the laws of photoelectric 

 action as they have revealed themselves by 

 experiments on the electrons emitted from 

 metals when illuminated by visible and ultra- 

 violet light. 



Perhaps the most striking feature of photo- 

 electric action is the existence of what has been 

 called the threshold frequency. For each metal 

 ■whose surface is in a definite state there is a 

 definite frequency rig, which may be said to 

 determine the entire photoelectric behavior of 

 the metal. The basic property of the thresh- 

 old frequency »]„ is this: When the metal is 

 illuminated by light of frequency less than n^ 

 no electrons are emitted, no matter how in- 

 tense the light may be. On the other hand, 

 illumination by the most feeble light of fre- 

 quency greater than n^ causes some emission. 

 The frequency n^ signalizes a sharp and abso- 

 lute discontinuity in the phenomena. 



Now let us inquire as to the kinetic energy 

 of the electrons which are emitted by a metal 

 when illuminated by monochromatic light of 

 frequency, let us say, n. Owing to the fact 

 that the emitted electrons may originate from 

 different depths in the metal, and may undergo 

 collision at irregular intervals, it is only the 

 maximum kinetic energy of those which escape 

 which we should expect to exhibit simple prop- 

 erties. As a matter of fact, it is found that 

 the maximum kinetic energy is equal to the 

 difference between the actual frequency n and 

 the threshold frequency n^ multiplied by 

 Planck's constant h. In mathematical sym- 

 bols, if V is the velocity of the fastest emitted 

 electron, m its mass, e its charge, and V the 

 opposing potential required to bring it to rest, 



eV = imt)^ ==:h(7i — »») . 



From this equation we see that the threshold 

 frequency has another property. It is evi- 

 dently that frequency for which kinetic energy 

 and stopping potential fall to zero. This sug- 

 gests strongly, I think, that the reason the elec- 

 tron emission ceases at w„ is that the electrons 

 are not able to get enough energy from the 

 light to escape from the metal, and not that 

 they are unable to get any energy from the 

 light. 



The threshold frequencies have another 

 simple property. If we measure the threshold 

 frequencies for any pair of metals, and at the 

 same time we measure the contact difference 

 of potential K between them, we find that K 

 is equal to the difference between their thres- 

 hold frequencies multiplied by this same con- 

 stant h divided by the electronic charge e. 



These results, as well as others which I have 

 not time to enumerate, admit of a very simple 

 interpretation if we assume that when illumi- 

 nated by light of frequency n the electrons 

 individually acquire an amount of energy hn. 

 We have seen that in order to account for ther- 

 mionic phenomena it is necessary to assume 

 that the electrons have to do a certain amount 

 of work w to get away from the emitter*. There 

 is no reason to suppose that photoelectrically 

 emitted electrons can avoid this necessity. Let 

 us suppose that this work is also definite for 

 the photoelectric electrons and let us denote 

 its value by hn^. Then no electron will be 

 able to escape from the metal until it is able 

 to acquire an amount of energy at least equal 

 to hrig from the light — that is to say, under 

 the suppositions made — until n becomes at 

 least as great as n^. Thus n^ will be identical 

 with the frequency which we have called the 

 threshold frequency, and the maximum en- 

 ergy of any electron after escaping will be 

 h (n — n„). 



The relation between threshold frequencies 

 and contact potential difference raises another 

 issue. We have seen that the contact poten- 

 tial difference between two metals must be 

 very nearly equal to the difference between 

 the amounts of work w for the electrons to 

 get away from the two metals by thermionic 

 action, divided by the electronic charge e. The 

 photoelectric experiments show that the con- 

 tact electromotive force is also nearly equal 

 to the differences of the threshold frequencies 

 multiplied by Ve- It follows that the photo- 

 electric work /in„ must be equal to the ther- 

 mionic work w to the same degree of accuracy. 

 We have to except here a possible constant 

 difference between the two. I do not see, how- 

 ever, how any value other than zero for such 

 a constant could be given a rational interpre- 



