DIATOMIC MOLECULES 73 



in the discussion of the processes occurring in more complex molecules. 

 The velocity of an electron accelerated by a voltage V is approximately 

 6 X IQpVv cm per sec, or 6 X IO^^a/f A per sec. Thus the time of 

 interaction of even a 1-volt electron with a small molecule is of the 

 order of 10~^^ sec, and for electrons of the voltages generally used the 

 time of interaction will be much less than this value for molecules of 

 molecular weight up to several hundred. The highest vibrational fre- 

 quencies of molecules (other than the H2 molecule) are of the order of 

 3000 cm""^, or 9.10^^ sec~^; most frequencies are one-third this value or 

 less. It is seen that the time of interaction of an electron of energy 

 greater than 10 volts with a molecule is at most one-thirtieth of the 

 shortest period of vibration of the molecule. The electron is too light 

 to transfer appreciable energy directly to the nuclei. We can safely 

 apply the Franck-Condon approximations (12) and state that the first 

 direct result of the electron impact is to raise the molecule to an excited 

 electronic state without change in either the internuclear distance or the 

 nuclear momentum. If we are to observe the results of this collision in 

 the mass spectrometer, it is, of course, necessary that the excited state 

 be an ionized state. It can be either the ground state or an excited state 

 of the ion. 



A set of possible potential functions for a diatomic molecule is given 

 in Fig. 1. Here, curve I represents the ground state of the molecule, 

 curves II and III are attractive states, and curve IV is a repulsive state 

 which dissociates to the lowest state for the separated atom plus ion; 

 curves V and VI represent two of the many possible states formed in 

 first approximation from excited states of the atom and ion. In accord- 

 ance with the Franck-Condon principle, transitions are probable only 

 to those parts of the potential curves between the lines a-a and h-h. We 

 note several possibilities. Transitions to state II will give only molecule 

 ions, and the minimum electron potential at which such ions appear 

 should be an accurate measure of the ionization potential of the molecule. 

 Transitions to state III can yield either molecule ions AB"^ or atom ions 

 A"*"; the appearance potential for AB"^ will be definitely larger than the 

 ionization potential of AB (to give the ion in this particular state), but 

 the appearance potential for A^ should give an accurate value for /(ab) + 

 ^(AB+) = ^(AB) + -^(A); and the ions A^ will be formed with low^ kinetic 

 energy irrespective of the magnitude of the electron energy. To obtain 

 transitions to state IV will require an electron energy several volts 

 greater than 2)(ab) + ^(X), and the resulting ions A"^ will have the 

 fraction 



W(B) 

 W(A) + m(B) 



