DIFFUSE MATTER IN SPACE 
375 
back to fetch more energy whilst the atom is passive. The shorter the life 
of the electron the more favourable is the chance of high temperature, since 
there is less opportunity for loss of initial energy and all loss is wiped out 
when the next life begins. 
(c) One source of loss of energy of the free electrons is scattering. Let 
us (very liberally) estimate the life of a free electron at 10 years. In that 
time the energy flowing through a square centimetre amounts to 9.10 6 ergs 
(for energy-density 10~ 12 ). To scatter this radiation completely it would 
be necessary to place the electrons contained in 5 gm. of matter as a screen 
(the coefficient of electron scattering being i by (53-5)). The screen con 
tains 1-5.10 24 electrons, so that each electron scatters 6.10 -18 ergs of 
stellar radiation or 2.10~ 28 units of momentum in 10 years. Even if the 
whole of this momentum were in a direction opposed to the motion of the 
electron its speed would be retarded less than 1 cm. per sec. The process 
(c) is evidently negligible. 
(d) Between expulsion and final capture an electron makes many 
encounters with atoms and is liable to undergo the switches described in 
§ 159. Switches involving loss of energy will occur in any case; switches 
involving gain of energy will be dependent on the presence of radiation 
available for absorption. The radiation concerned in switches is of lower 
frequency than the radiation which first expels the electrons from the 
atoms and determines their initial temperature; and interstellar radiation 
is relatively less rich in such frequency. Hence the gains of energy of the 
electron will by no means balance its losses, and in fact we cannot expect 
any appreciable part of the losses to be recovered. 
In § 159 we divided the spectrum emitted by electrons of given speed 
into two parts (a) due to switches, and (¡3) due to capture. The former 
represents the loss of energy during the lives of the electrons; from the 
latter we can compute the amount retained and given up on capture. As 
usual let hv 0 = |mF 2 , and let us consider the spectrum ¡3' formed by 
multiplying the intensities in spectrum ¡3 by v 0 /v. Since spectrum ¡3 
represents the whole energy emitted on capture, spectrum yS' represents 
the kinetic energy given up on capture; because the electron has only the 
kinetic energy hv 0 to lose, although it radiates hv by falling to an orbit of 
negative energy. By Kramers’ theory the intensity Q is constant up to 
the guillotine limit; hence the total intensities of the spectra are 
(«) Qv 0 , 
08') Q f lv ^dv = Qv O log^ 
where v x is the guillotine limit. Hence 
kinetic energy lost by electron 
1 
kinetic energy retained until capture 
log K/r 0 ) *