Temperature Radiation o; Gases. 



271 



is not an abrupt one, for, according to the quantum theory 

 of spectral emission, the electron may have an infinite 

 number of orbits distinguished by different quanta-numbers. 

 The theory of the stable orbits has been formulated by 

 Sommerfeld * in the following manner. Let n l9 n 2 denote the 

 rotational quantum numbers for an orbit, and n' the radial 

 quantum number, i. e. r, #, (j> being the coordinates of the 

 electron ; then, 



!©*-'*■ KI)^T A f(|>=" A 



the integration extending over the whole orbit. The energy 

 of the system is now given by the expression 



N 



A-h[- ( 



{n + ri +/(wi, n 2 , ri)} 



2 j, 7i t + n s 



where A = a constant, f(n, n) is a function, the value of 

 which decreases with increasing values of n and n' . 



The possible orbits can now be thus classified by assigning 

 different sets of values to n and n. 



Eotational Kadial 



quantum-no. quantum-no. 



Table II. 



Energy of the System 



Eemarks. 







m — 1 





 m-2 





 m-3 





 on— 4 







-(1.*) 



— (m, s) 



-(m,p) 

 -(3,d) 

 -(m,d) 



-(4,/) 



-(««/) 

 -(5,*) 



»')}i 



This is the orbit which the 

 electron possesses when it 

 is subject to no stimulus. 

 m:>l, the s-orbits. 



The ^j-orbits. 



m>2. 



The c?-orbits. 



The /"-orbits. 



w>4. 



The /('-orbits. 



m >- 5. 



(1, s), (2,p), (3, d), . . (m, s), . . are the familiar expressions 

 which, in Paschen's notation, denote the terms of which a 

 * Sommerfeld, Verh. d. Deutsch. Phys. Ges. vol. xxl (1919). 



