210 RADIATION BIOLOGY 



tightly bound molecule with very light vibrating atoms, it has the excep- 

 tionally great value of 0.52 ev. Thus vibrational levels are much more 

 closely spaced than are electronic levels. It is an interesting and impor- 

 tant fact that the vibrational state corresponding to w = still has 

 Evib = }4.hv^ih. Thus the lowest state permitted by the quantum theory 

 is one of positive energy; that energy, }ihv^,ib, is called the zero-point 

 energy. 



Even though the electronic and vibrational states are specified, 

 characterization of the state of a molecule is incomplete, for it may 

 be in one of many possible rotational states. The rotational state is 

 specified simply by the rotational quantum number J, which must be a 

 positive integer or zero, and the rotational energy is given (approx- 

 imately) by 



Erot = hVrotJ{J + 1) 



It is to be noted that the lowest rotational state is effectively one of no 

 rotation, and that the spacing of the rotational levels increases as the 

 excitation (and therefore J) increases. 



As an example of the foregoing, some of the energy levels of the N2 

 molecule are illustrated in Fig. 3-2. It is interesting to note that hv^ib for 

 this molecule is 0.29 ev, so that in the process 



Hg* -f- N, ^ Hg (6«Po) + N; 



discussed in Sect. 3-le the excited state meant by Ng is doubtless the first 

 excited vibrational level of the ground electronic state. [The 6^Pi — 6^Po 

 energy difference is 0.22 ev, so that the process is endothermal by 0.07 ev. 

 This energy must be provided by the translational and chiefly rotational 

 energy of the colliding N2, but since it is only about twice the mean 

 thermal translational energy, about one-tenth of the N2 molecules have 

 at least the required amount. It should not be supposed, however, that 

 one-tenth of the collisions between Hg* and N2 result in the transi- 

 tion, for the necessity of providing an activation energy (cf. Sect. 3-2c) 

 diminishes this fraction considerably]. 



Transitions, by emission or absorption of light, between energy levels 

 of a molecule give rise to its characteristic spectrum. Transitions 

 between two different electronic states can be made, however, in a variety 

 of combinations, according to the particular vibrational and rotational 

 levels of the initial, and of the final, state. The array of wave lengths 

 comprising the various possible combinations is an intricate one, the 

 spectral lines being grouped into a series of hands, each of which corre- 

 sponds to a definite vibrational transition with differences only in rota- 

 tion. The band spectra of diatomic molecules arising from electronic 

 transitions lie in the visible or ultraviolet region. Transitions between 

 vibration-rotation levels of the same electronic state are also possible (if 



