THE COEFFICIENT OF OPACITY 
219 
149. Preliminary calculations show that, whereas in all cases the ideal 
absorption coefficient is enormously modified, the modification of the 
emission coefficient is small in most stars, and in any case it can be left 
to be attended to in a second approximation. At first sight it seems that 
the figures given for iron in § 147 are in contradiction to this since it 
appears that 70 per cent, of the K electrons are in their places and only 
30 per cent, of the ideal K emission for iron is operative. But the calcula 
tion of § 147 referred to the true absorption coefficient and we now have 
in mind the astronomical opacity (§ 77), which is less dependent on the 
K processes*. However, we do not insist here that the modification of the 
emission coefficient is negligible but that it is small in comparison with the 
modification of the absorption coefficient by a factor T ^ I ?TÏÏ . Accordingly, 
the stellar opacity will approximate to the law k oc pfri, and not to k 
independent of p. 
Now consider the effect of temperature. The number of electrons which 
in given time encounter a particular ion, besides being proportional to the 
electron-density will be proportional to their mean velocity V and there 
fore to T^. Further, granting an encounter, the chance of capture will 
depend on the speed of the electron. Presumably fast electrons will be 
more elusive than slow ones; we therefore set the chance of capture 
proportional to y_ x 
or to T~^ x . We can only determine x by following up some special theory 
of capture, so for the present we leave it indefinite. When a capture 
occurs the emission of energy is equal to the difference between the energy 
of the free electron and the negative energy of the level which it will 
occupy in the atom. The free energy is proportional to T and the energy 
of the level is presumably roughly proportional to T f. Combining these 
temperature factors, the emission per ion will be proportional to 
R T? ~ i x ) 
and the absorption per ion is the same. To obtain k we must divide the 
absorbed energy by the total energy traversing the material, which is 
proportional to T 4 . Hence kai /flT \+ix (149-1). 
The astronomical result that k is nearly constant for a series of stars 
of constant mass requires that approximately k must be a function of 
* In § 79 we showed that it was not important to consider frequencies greater 
than IRT/h. Hence in a star in which the atoms are ionised down to an energy - 
level - 1RT there will be no appreciable modification of the ideal emission coefficient. 
f Alternatively, the captures chiefly contributing to the opacity are those yielding 
radiation of frequency 2-5 RT/h to 7 RT/h (§ 79). The corresponding quantum is 
therefore proportional to T.