Spectra of the Elements, and Structure of the Atom. 559 



Let W be the energy which is emitted during the formation 

 of a hydrogen atom. Then W, the corresponding energy for 

 an atom containing a nucleus ~Ne and a ring of n electrons, is 



w=™w (n-jS„Y 



Bohr takes, as a criterion, that the formation of one system 

 from another is possible if, and only if, the value of W is 

 greater for the new system than for the old. Thus, if a 

 system with n electrons can lose an electron, 



f(n, N) <f(n- 1,N), 



and if it can gain one, 



'i»,s)</(»+a) 



/ 1 A 2 



where f(n,l$) = n{ N— - S» J . 



We may consider the various systems with one ring in turn, 

 identifying them with the elements of the Periodic Table. 



(1) Lithium, N = 3. 



f(3, 3) = 17-607, /(4, 3) = 16-694, /(5, 3) = 13-178, 

 /(2, 3) = 15-13, /(1,3) = 9. 



f(3, 3) is the largest value, and therefore lithium should be 

 an inert element like helium. 



(2) Beryllium, N = 4. 



/(4, 4) = 37-037, /(3, 4) = 35-142, /(5, 4) = 34-414. 

 Beryllium should also be inert. 



(3) Boron, N = 5. 



f\5, 5) = 65-65, M, 5) = 65*38, /(6, 5) = 60-39. 



Boron might take up one electron, but could not retain it 

 under ordinary circumstances. 



(4) Carbon, N = 6. 



f(<o, 6) = 104-466, /(5, 6) = 106*885, 

 /(4, 6) = 101-724, /(7, 6) = 95-578. 

 Oarbon should be monovalent and of a metallic nature. 



(5) Nitrogen, N=7. 



/(7, 7) = 154-315, /(6, 7) = 160-536, /(5, 7) = 158-120. 

 y\4, 7) = 146-068, /(8, 7) = 140-784. 



and nitrogen should be divalent and metallic. 



2P2 



