710 BELL SYSTEM TECHNICAL JOURNAL 



The contrast between this and the classical situation is evidently 

 enormous. Where formerly we were asked to think of the electrons 

 in a metal at usual temperatures as being distributed Maxwell-wise 

 about a very modest mean energy, say about 0.02 of an equivalent 

 volt, we are now invited to conceive them as distributed all through 

 a range of energies extending from zero up to as much as half a dozen 

 equivalent volts, and more abundantly the nearer one approaches 

 to the top of this range, abruptly though the distribution ceases 

 when the very top is reached. This is "zero-point energy" with 

 a vengeance ! 



The pressure of the electron-gas is related to the energy-per-unit- 

 volume by the equation valid also in the classical theory: 



and therefore varies like the total energy — starting from a value 

 absurdly high at the absolute zero (hundreds of thousands of atmos- 

 pheres) and increasing therefrom very slowly at first, though according 

 to a T'^ law, as the temperature rises. I do not know of any manometer 

 for measuring internal electron-pressures, but if anybody should 

 invent one he had better make it strong. 



There is manifest ground for doubting these remarkable proposals: 

 thermionic data seem to show that the work-function which opposes 

 the egress of the electrons from a metal is itself less than half-a-dozen 

 volts (in the usual measure), for some metals less than two — what 

 then keeps these fast electrons confined within the metal? It turns 

 out, however, that in augmenting the vis viva of the electrons the new 

 theory also raises the top of the wall which they must overleap. 

 Here indeed we meet with the first of the new experiments which tend 

 to confirm the new theory. 



Thermionic Emission 



The simplest theory of the thermionic current is, that it consists of 

 all the electrons belonging to the interior electron-gas which fly 

 against the boundary-surface of the metal with velocities such that the 

 component u thereof perpendicular to the boundary-surface is great 

 enough to make the "energy-component" ^mii^ greater than a constant 

 Wa — the said constant being interpreted as the work-function or the 

 retarding potential-drop at the edge of the metal. The thermionic 

 electrons are those which swim up to the surface with an outward- 

 bound velocity-component so large, that by means of the kinetic 

 energy of their outward motion they can climb over the wall. 



