137
Many aspects of radiation are most easily understood by thinking of radiation as a wave. Others need a different picture—that of
radiation as discrete packets of energy, photons. The idea of a wave
that is also discrete energy units is not intuitive; it is another of
the results of quantum theory that do not correspond to ordinary
experience. The energy E ph of a photon of radiation of frequency ν
or wavelength λ is
E
h
hc
ph =
=
ν λ
(4.55)
where h is Planck’s constant (6.626 × 10
−34 J·s) and c is the speed of
the radiation. Thus radiation of a given frequency has photons of
fixed energy, regardless of its intensity; an intense beam simply has
more of them. This is the key to understanding reflection, absorption, and transmission.
Why aren’t metals transparent?
Electrons in materials circle their parent atom in orbits with discrete energy levels, and only two can occupy the same level. Metals
have an enormous number of very closely spaced levels in their
conduction band; the electrons in the metal only fill part of this
number. Filling the levels in a metal is like pouring water into a
container until it is part full—its surface is the Fermi level—and
levels above it are empty. If you “excite” the water—say, by shaking
the container—some of it can slosh to a higher level. If you stop
sloshing, it will return to its Fermi level.
Radiation excites electrons, and in metals there are plenty of
empty levels in the conduction band into which they can be excited.
But here quantum effects cut in. A photon with energy hν can
excite an electron only if there is an energy level that is exactly hν
above the Fermi level—and in metals there is. So all the photons
of a light beam are captured by electrons of a metal, regardless of
their wavelength. Figure 4.68 shows, on the left, what happens to
just one.
What next? Shaken water settles back, and electrons do the same.
In doing so they release a photon with exactly the same energy that
excited them in the first place, but in a random direction. Any
photons moving into the material are immediately recaptured, so
none makes it more than about 0.01µm (about 30 atom diameters)
below the surface. All, ultimately, reemerge from the metal surface—
that is, they are reflected. Many metals—silver, aluminum, and
stainless steel are examples—reflect all wavelengths almost equally
Optical Behavior
Many aspects of radiation are most easily understood by thinking of radiation as a wave. Others need a different picture—that of
radiation as discrete packets of energy, photons. The idea of a wave
that is also discrete energy units is not intuitive; it is another of
the results of quantum theory that do not correspond to ordinary
experience. The energy E ph of a photon of radiation of frequency ν
or wavelength λ is
E
h
hc
ph =
=
ν λ
(4.55)
where h is Planck’s constant (6.626 × 10
−34 J·s) and c is the speed of
the radiation. Thus radiation of a given frequency has photons of
fixed energy, regardless of its intensity; an intense beam simply has
more of them. This is the key to understanding reflection, absorption, and transmission.
Why aren’t metals transparent?
Electrons in materials circle their parent atom in orbits with discrete energy levels, and only two can occupy the same level. Metals
have an enormous number of very closely spaced levels in their
conduction band; the electrons in the metal only fill part of this
number. Filling the levels in a metal is like pouring water into a
container until it is part full—its surface is the Fermi level—and
levels above it are empty. If you “excite” the water—say, by shaking
the container—some of it can slosh to a higher level. If you stop
sloshing, it will return to its Fermi level.
Radiation excites electrons, and in metals there are plenty of
empty levels in the conduction band into which they can be excited.
But here quantum effects cut in. A photon with energy hν can
excite an electron only if there is an energy level that is exactly hν
above the Fermi level—and in metals there is. So all the photons
of a light beam are captured by electrons of a metal, regardless of
their wavelength. Figure 4.68 shows, on the left, what happens to
just one.
What next? Shaken water settles back, and electrons do the same.
In doing so they release a photon with exactly the same energy that
excited them in the first place, but in a random direction. Any
photons moving into the material are immediately recaptured, so
none makes it more than about 0.01µm (about 30 atom diameters)
below the surface. All, ultimately, reemerge from the metal surface—
that is, they are reflected. Many metals—silver, aluminum, and
stainless steel are examples—reflect all wavelengths almost equally
Optical Behavior