Photoelectric and Photochemical Action. 477 



The Energy abstracted per Atom liberated. 



Consider any condensed form of any substance, bounded 

 by a surface, which emits any monatomic gas under the 

 influence of illumination. 



Let £=the mean internal kinetic energy of these atoms, 

 i. e. the kinetic energy they possess when in the 

 condensed form. 

 W = the average work done by each atom in escaping 

 from the substance. 

 w = the average change of total energy which accom- 

 panies the escape of a single atom. 



Then -x RT is the mean external kinetic energy£(?'. e. after 



escaping) of an atom at temperature T and 



2c=|RT~|+W (1) 



Let <j)(y) denote the mean energy which each atom, liber- 

 ated under the influence of monochromatic radiation of 

 frequency v, has acquired from the radiation at the moment 

 of liberation. The kinetic energy of each atom immediately 

 before emission is thus <j>(y) + £, if the contribution to f arising 

 from the radiation is treated as negligible (see last paragraph), 

 and the mean kinetic energy each atom carries away from 

 the surface of the substance is 



T v = <j>(v) + g-W = <t>(v) + ?UT--w. . . (2) 



If the substance is enclosed by an isolating boundary, so 

 that the space between the substance and the boundary is 

 initially vacuous, there will ultimately be equilibrium cha- 

 racterized by some constant temperature, let us say T. The 

 body will be emitting atoms under the influence of the 

 complete radiation characteristic of T, and these will be 

 returning to the body on account of their kinetic motions. 

 The two processes balance, so that the state is invariable. 

 By moving a piston transparent to radiation, the quantity of 

 emitted gas can be varied without changing the quantity of 

 radiation, so that, as before*, if n is the number of liberated 

 atoms per unit volume, 



n = A,e^ R1 - , (3) 



where A is a quantity which is characteristic for the sub- 

 stance but is independent of T. The number N x of liberated 



* O. W. Richardson, Phil. Mag. vol. xxiii. p. 619 (1912). 

 Phil. Maq. S. 6. Vol. 27. No. 159. March 1914. 2 K 



