136
The Source of Stellar Energy [ch. iv
We must suppose that one of the heavy atoms in a star’s interior first
begins to change into radiation through one of its bound electrons falling
into the nucleus, and coalescing with one of the nuclear protons so that both
are annihilated. It is immaterial whether the whole atom changes into
radiation at once or through a succession of comparatively slow changes. In
either case the process of annihilation is likely to consist of a series of
events in each of which a single proton and a single electron are annihilated
simultaneously.
As we have seen, the energy set free by the annihilation of a proton of
mass M and an electron of mass m is (m +M)C 2 , which is equal to 0*0015 ergs.
In accordance with general quantum principles each such annihilation must
result in the production of a single quantum of radiant energy of frequency v
given by
hv — 0-0015 ergs,
so that the frequency v is 2*3 x 10 23 and the wave-length is 1*3 x 10~ 13 cms.
Each time a proton and electron are annihilated a splash of radiant energy
of this wave-length and of total energy 0*0015 ergs is produced, and sets off
to travel through the star until, after innumerable absorptions and re
emissions, it reaches the star’s surface and wanders off into space. Except
for being many thousands of times more powerful, each splash is similar to
the splashes produced by radioactive material in the spinthariscope. The
great energy of the splashes is to some extent counterbalanced by their rarity.
In the sun, for instance, only about one atom in every 10 17 annihilates itself
each hour.
As this very high-frequency radiation travels through a star, it may be
either scattered or absorbed when it meets an atom. Absorption can only be
by complete quanta; the absorption of a quantum ejects an electron with a
velocity representing kinetic energy of 0'0015 ergs, and so equal to 0*99999985
times the velocity of light. When this electron strikes an atom a new quantum
of radiation is emitted whose energy, and therefore also wave-length, is equal
to that of the original radiation. The hardness of the radiation is thus
unaffected by absorption and re-emission. The scattering of the radiation, on
the other hand, is readily shewn to produce a softening of its quality, just as
in the ordinary Compton effect, and a succession of such scatterings will
increase the wave-length of the radiation until it becomes indistinguishable
from ordinary temperature radiation.
Newly generated radiation, in spite of its extreme hardness, will not
penetrate far through the interior of a star without being changed in this way,
so that we should expect the radiation emitted from the surface of a star to
be ordinary temperature radiation, retaining no traces of its origin as radiation
of extremely short wave-length.
On the other hand, astronomical bodies exist which are transparent to
ordinary light and so, à fortiori, must be transparent to this high-frequency