508 Quantum Mechanical Basis of Molecular Spectra /27 : 2 



Suppose the photon is in the green region of the spectrum, with a 

 wavelength of 5,500 A. Then 



A = 600 m/x = 6 x 10" 5 cm 



The energy of the photon is 



_, he 6 x lO" 27 x 3 x 10 10 . in 12 



E = A = c^TlO^ = 3 X 10 ergS 



The time At during which there is an uncertainty AE in the atomic 

 energy comparable to E is 



A* » = 77 r— r = 3 x 10 -16 sec 



(2tt£) (277C) 



This indicates that the emission or absorption of such a photon must 

 take place in 10 _15 sec or less. During this period of time, it is possible 

 for the energy to have any intermediate value between E ± and E 2 . 

 (For shorter periods of time, the energy may vary still more. The law 

 of conservation of energy is not valid for such short periods of time. 

 This law describes only averages over periods of time long compared 

 to 10" 15 sec.) 



The foregoing example indicates that the statement that E 1 and E 2 are 

 average values means that the average is taken over periods of time 

 which are long compared to 1 " 15 sec. It is extremely difficult to measure 

 periods of time as small as this. The average energy is the one which 

 would be measured by almost any method except the emission or absorp- 

 tion of a photon of energy E. 



As stated previously, certain quantities such as time and energy 

 cannot both be known precisely. Other quantities can be known at the 

 same time. (These latter are called commutable, in the language of 

 quantum mechanics.) One set of variables, all of which can be known 

 at the same time for an electron, consists of its energy, its total angular 

 momentum, the projection of its total angular momentum on any given 

 axis, and its orbital angular momentum. Having read that electrons 

 are not restricted to orbits, the reader may justifiably feel surprised to 

 see the word "orbital" used here, and he also may feel puzzled at the 

 difference between total angular momentum and orbital angular 

 momentum. Perhaps the next paragraph may make these statements 

 a little clearer. 



Many small particles, such as electrons, have an intrinsic angular 

 momentum called spin. It is convenient to think of the electron spinning 

 like the earth about some internal axis. This leads to certain difficulties 

 with the theory of relativity, so most physicists today simply mumble 

 "intrinsic angular momentum" and let it go at that. In addition, the 



