234
THE COEFFICIENT OF OPACITY
undoubtedly contains a great deal of truth, the details are as yet somewhat
tentative, and, moreover, in its present form, it accounts for only a small
part of the stellar opacity.
Comparison with Laboratory Experiments.
161. If Kramers’ theory were merely a speculation as to the manner
in which classical laws pass over into quantum laws, it would not greatly
disturb us to find astronomical results partly discordant with it. But the
theory has been compared with laboratory experiments and found satis
factory, so that astronomical conflict with Kramers’ theory is virtually
a conflict with laboratory experiment.
In an X ray tube a stream of electrons, all with the same velocity F
acquired under a known fall of potential, falls on the material of the anti
cathode. In this case the atoms have their full complement of electrons
so that there is no opportunity for capture, and only spectrum a can be
emitted. Within the anticathode the electrons gradually lose their energy
chiefly by other dissipative causes and only to a small extent by the radia
tion of spectrum a. The total spectrum is therefore due to electrons with
all velocities from 0 to F. We can measure the radiation J V dv corre
sponding to an initial velocity F, and (J v + AJ„) dv corresponding to an
initial velocity F + AF; then (A J v )dv represents the spectrum emitted
by the electrons whilst their velocity falls from F + A F to F —after which
fall they are in a position to radiate J v just as if they were first entering
the anticathode*. Hence the spectrum due to electrons of the same
velocity F is of intensity Q v dv, where
<2„ = AJ„ = ^.-AF (161-1).
and Q v should be given by (155-42) provided that s represents the number
of atoms per sq. cm. in a thickness of anticathode such that the average
electron velocity diminishes by A F in traversing it.
The best experimental determinations of J v appear to be those of
H. Kulenkampfff. Due correction has been made for the absorption by
the anticathode of the radiation emitted within it. Deriving Q v by (161-1),
these experiments show that the spectrum Q v is of uniform intensity up
to v 0 and ceases abruptly at v 0 . Further, dJJdv 0 is proportional to Z and
independent of v 0 , so that dJJdV is proportional to ZV . According to the
Thomson-Whiddington law the decrease of velocity A F in a sheet contain
ing a constant number of atoms 5, is proportional to Z/F 3 ; hence by
* This is only true because the proportion of electrons concerned in radiating
spectrum a is small; the electrons radiating At7„ have their velocities suddenly
reduced by a large amount and can take little part in the further radiation J„.
f Ann. d. PhysiJc, 69, p. 548 (1922).