THE COEFFICIENT OF OPACITY
235
(161*1) Q„ is proportional to (ZV) x ( Z/V 3 ) = Z 2 /V 2 in agreement with
(155-42). Kramers’ result is thus confirmed in every detail.
It remains to test the absolute value of Q. This is more difficult since
it depends on absolute instead of differential experiments. According to
a direct comparison the experiments give about twice as much radiation
as the theory ; but as Kramers points out they are not strictly comparable
and the actual agreement is probably closer. In any case the experimental
confirmation of this part of Kramers’ theory is so close as to constitute
a remarkable triumph for the theory.
162. One doubtful point remains which may conceivably have astro
nomical importance. In addition to the radiation here described Kulen-
kampff found a considerable emission at or very near to the limiting
frequency v 0 ; that is to say, J v does not rise uniformly from zero value
at v 0 but starts almost abruptly at a finite value. This radiation, which he
calls spectrum B, must be emitted by electrons which just lose their whole
energy. Presumably they may be considered as captured in high quantum
orbits; if so, the atoms capturing them become negatively charged*.
But there is no provision for the corresponding radiation in either spectrum
a or spectrum /3 of the classical theoryj*. It may be that capture in ordinary
orbits being blocked, the spectrum ¡3 heaps itself up at the limit v 0 ; but
this is not in accordance with Kramers’ ideas. The slight reference to
spectrum B in Kramers’ paper ( loc . cit. p. 870) does not seem to elucidate
the phenomenon. We cannot foresee what will happen to this radiation
when we are dealing with ions instead of complete atoms, so it is impossible
to say what part (if any) it will play in stellar opacity.
163. The spectrum between v 0 and v x is not emitted under laboratory
conditions ; and the theoretical predictions cannot be tested directly. But
since coefficients of emission and absorption are connected by Einstein’s
relation (38-4) we may make equivalent tests on the corresponding ab
sorption spectrum. Consider the emission and absorption of a line w T hich
replaces a stretch of continuous spectrum of extent fip x in energy units
or fifjjh in frequency units (cf. (159-3)). Here ifj x = - Xx is the negative
energy of a 1-quantum orbit. To calculate the emission for this line dv
must be replaced by fifjjh in (155-42). Consider a cubic centimetre of
material containing s fully-ionised atoms and n free electrons of velocity
V to V + dV. In unit time n' V electrons will traverse the cubic centimetre
so that the emission per cu. cm. per second is by (155-42)
m'Vfi/t! 32tt 2 W
h Zy/Zc 2 m 2 V 2 '
* It is known from positive ray experiments that atoms can become negatively
charged.
f The part of spectrum /3 assignable to the high quantum orbits is extremely small.
f