High Frequency Spectra. 205 



except for the Pt.aj line. The apparent discrepancy can be ex- 

 plained by the fact that these authors were unable to distinguish 

 between the Pt.a2 line and the Ir.a^ line. The writer has found 

 that if the K spectra of Pt. and W are photographed on the 

 same portion of a film, it is impossible to recognise as separate 

 lines, the W/? (X=-1843) and Pt.ai(.\=-1851) 



Theory of Lines. — The K series of an element is excited when 

 an electron is ejected from the K ring of the atom. If this 

 electron is replaced from the L ring of the atom, the energy so 

 freed gives rise to the a^ line. If it is replaced from an electron 

 from the L' ring (an elliptical orbit), the a^ line is excited. Re- 

 placements from the M and N rings give rise to the p and y 

 lines respectively. 



Moseley's formula, ~— (N - 1)^(1/P- 1/2-), for the wave number v 

 is. 



of the Ktti line, which accurately represents the observed values 

 for low values of N, fails for elements of higher-atomic number. 

 (R is here Rydberg's constant, N the atomic number of the 

 element.) The value of the wave length of the Pt.ai line from 

 this formula would be .2049 x lO^ cm. 



Sommerfeld has developed a formula for the wave number 

 ^( = 1/A), by considering the effective nuclear charge for the 

 K and L rings as (N- 1.6) and (N-3.5) resp. and by taking into 

 account the relative masses of the electrons in consequence of 

 their velocity. The formula is : — 



v/R = ?^( >y/i - ^'(N - 3-5)2 - /y/i _ a\N - l-Qf) 



where «=— r- e, c, h being the charge on the electron, the 



velocity of light and Planck's constant respectively. Hence 

 a2« 5.3088 X 10-5. 



This formula gives X for Kai of Pt. = -1837 x 10.-«cm. 



A formula due to Kroo and Sommerfeld fits the observed 

 value more accurately still. In this, before the passage of the 

 atom, which gives rise to the Ka^ line, the K ring is considered 

 as a 1 quantum ring with 2 electrons, the L ring as a 2 quanta 

 ring with 9 electrons. After the passage of the electron, the 

 K ring is a 1 quantum ring with 3 electrons, and the L ring 

 as a 2 quanta ring with 8 electrons. By calculating the energy 



