464 Prof. E. K. Rideal on the 



of the phosphine molecule, u x the mean velocity of the 

 molecules negligible in comparison with u 2 =lc the velocity 



of the light quanta, — - — ■ = the number of quanta per unit 



. 8ttp 2 *" 



volume = — 5- e at. 

 a 6 



Hence the reaction velocity constant 



dn 8tt 2 o- _** 

 = — = - — v . e at Sv. 

 dt > c 



di 



hv 



8Xe~w 9 



since 



C C V 



v =.~ and — Sv = — ,§X = — BX. 

 X X 2 c 



Taking the value of SX equal to the actual molecular 

 diameter cr', the velocity coefficient becomes equal to 



dn SttVo-V 2 l* 



— = , v e at. 



dt c 2 



The actual diameter of a phosphorus molecule cr' is 



ca. 2*3.10 -8 cm., whilst the effective diameter in reaction 



with light quanta is the diameter of the orbit of the reacting 



valency electron. The diameter of the orbit in the case of 



the hydrogen atom is 5'5.10~ 9 cm., and since the atomic 



number of phosphorus is 15, the electron orbit diameter 



5*5. 10~ 9 

 will be ca. - — ~ — = O37.10~ 9 ; hence a' = 62 a. 



JLO 



The velocity V of an electron circulating in the phosphorus 

 atom in an orbit of effective diameter a and with a frequency v 

 is 7Tcrv ; hence 



or the velocity coefficient 



dn 62x8.V 2 - hv - 496 V 2 _ *? 



-r- = ■ 5 .ve k t= ^— . ve at. 



dt c 2 c z 



Bohr has calculated the velocity of the electron in the 

 common orbit of the hydrogen molecule, and finds it equal 

 to 3*62. 10 7 cm. per sec. In the phosphorus atom, of atomic 

 number 15, this velocity is certainly higher. According to 

 Sanford and Kunz (Phys. Rev. ix. p. 383, 1917, and xii. 

 p. 60, 1918) the electron velocity is approximately pro- 

 portional to the atomic number, which would assign a value 



