A ship heading into a rough sea runs most risk of damage, and its
passengers most risk of discomfort, when its length is about equal to
the length of the waves. Short waves disturb a short ship and long
waves a long ship, but a long swell does little harm to either. But
this provides no real analogy with the effects of radiation, since
the wave-length of radiation which breaks up an electrical structure
is hundreds of times the size of the structure. The nautical analogy
to such radiation is a very long swell indeed. As a rough working
guide we may say that an electrical structure will only be disturbed
by radiation whose wave-length is about equal to 860 times the
dimensions of the structure, and will only be broken up by radiation
whose wave-length is below this limit[14]. In brief, the reason why
blue light affects photographic plates, while red light does not, is
that the wave-length of blue light is less, and that of red light is
greater, than 860 times the diameter of the molecule of silver bromide;
we must get below the “860-limit” before anything begins to happen.
[14] The mathematician will readily see the reason for this rule, which
is, in brief, as follows: the energy needed to separate two electric
charges + _e_ and - _e_, at a distance _r_ apart, is _e_²/_r_, and the
energy needed to re-arrange or break up a structure of electrons and
protons of linear dimensions _r_ will generally be comparable with
this. If λ is the wave-length of the requisite radiation, the energy
made available by the absorption of this radiation is the quantum
_hC_/λ. Combining this with the circumstance that the value of _h_ is
very approximately
_e_²
860 —————,
_C_
we find that the requisite wave-length of radiation is about 860 times
the dimensions of the structure to be broken up.
When an atom discharges its reservoir of stored energy, the light
it emits has necessarily the same wave-length as the light which it
absorbed in originally storing up this energy; the two quanta of energy
being equal, their wave-lengths are the same. It follows that the light
emitted by any electrical structure will also have a wave-length of
about 860 times the dimensions of the structure. Ordinary visible light
is emitted mainly by atoms, and so has a wave-length equal to about 860
atomic diameters. Indeed it is just because it has this wave-length
that the light acts on the atoms of our retina, and so is visible.
Public-domain text, read in full here on John Shaqi.
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