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RADIATION BIOLOGY 



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INTERATOMIC DISTANCE, A 



Fig. 3-3. Potential curves of some of the 

 electronic states of molecular hydrogen. 



total energy is essentially the sum of the energies of the two separated, 

 isolated atoms. In the case of two atoms which attract each other, and 

 therefore form a stable molecule, if r is diminished E will at first decrease. 

 When r becomes very small, however, the atoms interpenetrate and repel 

 each other (the electron shells no longer shield the respective positive 

 nuclear charges and prevent their Coulomb repulsion) , so that as r further 

 decreases E ceases to decrease and finally rapidly increases. This 

 behavior of E{r) gives rise to a characteristic "potential curve" such as 

 the lowest curve in Fig. 3-3. The presence of the minimum in this curve 



indicates the formation of a stable 

 diatomic molecule, and, indeed, the 

 value of r at that minimum (called 

 rj is just the interatomic separa- 

 tion in the non vibrating molecule. 

 In certain electronic configura- 

 tions the two separated atoms, as r 

 decreases, do not attract each other; 

 instead they repel. The distance 

 at which the repulsion sets in varies 

 considerably and depends on the 

 nature of the repulsive force. An example of this type of potential curve 

 is the second lowest curve in Fig. 3-3. The absence of a minimum means 

 that a stable molecule is not formed. 



The state of lowest energy of a stable molecule is that at the minimum 

 of the potential curve. If, for a molecule having slightly greater energy, 

 i.e., r differing shghtly from re, the constraint on vibration is suddenly 

 removed, the molecule will vibrate about r^. The total energy will remain 

 constant, a certain fraction of it varying between potential energy and 

 kinetic energy of vibration. The value of E at r,, is accordingly con- 

 sidered to be the electronic energy of the state corresponding to the partic- 

 ular potential curve, and the height of the actual energy above the min- 

 imum to be the vibrational energy Evib- Molecular vibration is analogous 

 to the frictionless motion under the influence of gravity of a small ball in a 

 hole having the contour of the potential curve. According to ciuantum 

 theory, the possible energy levels (represented by horizontal lines stretch- 

 ing across the curve) are located at intervals of /iJ^,* above the lowest 

 level, which in turn is located at a height of ^-z^Vvib above the minimum 

 (cf. Fig. 3-6). This representation is far more useful than the simpler 

 type shown in Fig. 3-2. In the case of a repulsive curve, there are, of 

 course, no vibrational levels. Rotational levels can also be incorporated 

 into potential curves, but only at the expense of greater complexity of the 

 representation (cf. Herzberg, 1950). 



The dependence of E on r is different for each electronic state of the 

 molecule. This statement is made clearer upon consideration of the fact 



