Photons
The beginning of quantum mechanics can be
traced back to Max Planck's discovery (around 1900) that the known blackbody
radiation could be explained by assuming that the energy had bursts hf, where h
is a constant called Planck's constant, 6.63 x 10-34 Joule second
and f is the frequency of the radiation. He thought it was a peculiarity of the
radiating matter; Einstein later interpreted it as a property of light itself.
He analyzed the photoelectric effect, and later experiments confirmed his
analysis. Much later, Louis de Broglie figured that if light is or acts like a
particle, maybe the electron is or acts like a wave. His idea turned out to be
correct, and soon after, quantum mechanics was in full bloom.
So using E for energy, we have the energy of
a photon
E = hf = hc/l (As you
know, the speed of any wave is lf, and light speed is c. So replace f with c/l to get E=hc/l.)
It is fairly common to use electron-volts as the energy unit and nanometers (10-9
meters) for wavelength, so it is useful to know that hc = 1240 eV∙nm.
Light energy is always multiples of the
photon energy. You cannot have a fraction of a photon. So this is particle-like
behavior. Whether you say it is a particle or acts like a particle is a matter
of style. Light has both wave and particle characteristics. (So do all the
"particles;" we should call them all wavicles.)
As you know from relativity, energy is mass
and mass is energy, according to E = mc2, so if we write mc2
= hc/l , we find that a photon acts like mass h/(cl ). I say
"acts like" because it is customary to use the term mass as the
measured value when the thing is at rest. In that sense, the photon has zero
mass. Some people say zero rest mass to avoid any confusion.
The momentum of a photon is h/l (found by
multiplying the above mass by velocity c). You can use this to solve collision
problems, for example a collision between an electron and a photon. It works
just like an elastic collision in mechanics except that if the photon gives
some energy to the electron, then the photon after collision will have a longer
wavelength. Compton calculated the D l for the case of the electron initially at rest and
found
D
l
= (h/mc)(1-cosq ) where q is the angle of the scattered photon measured from
the initial photon direction. (Click on
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