Light Radiation
Objective: To work with the laws of electromagnetic radiation from hot bodies, to
distinguish blackbody radiation from atomic and molecular absorption of light, and to
apply Wien’s law to measure the radiation temperature of the Earth’s atmosphere and
surface, the radiation temperature of the atmosphere and surface of Mars, and the
effective temperature of Phobos, one of the moons of Mars.
Equipment: Example of spectra from various sources and plots of the emission intensity
versus wavelength for a selection of planetary bodies.
Introduction: In 1865, James Clerk Maxwell, while formulating the theory of
electromagnetism, discovered that the logic of his theory led to the possible existence of
electromagnetic waves which would move at the speed of near 300,000,000 meters per
second. This, he noticed, was the speed of ordinary visible light. Moreover, the other
properties of light were consistent with his new waves. The various colors in the rainbow
are different frequencies of visible light. Maxwell predicted a wide range of
electromagnetic waves, with light as only one example. Today, much of advanced
technology uses many of these waves Maxwell foresaw.
Electromagnetic waves are produced by wiggling charges. We say the wave is ‘emitted’
by accelerating charges (when a charge “wiggles,” it is essentially accelerating in one
direction, and then the other). Such waves carry energy away from the wiggling charges,
and as the wave travels along, any other charges it passes though will ‘absorb’ some of
the wave energy and start accelerating. (The description changed after 1900, when
Planck and Einstein realized that the energy is actually emitted and absorbed only in
indivisible bundles or quanta called photons, each of which carries a certain amount of
energy. The energy of the photons is proportional to the frequency of the wave.)
Since ordinary matter is made of atoms with charges within, ordinary matter can emit and
absorb electromagnetic waves. In fact, ordinary matter made from lots of atoms at a
finite (greater than absolute zero) temperature MUST radiate electromagnetic energy. At
a finite temperature, the atoms are wiggling. This makes the easy-to-move electrons
inside wiggle also, and they then emit photons at various energies (frequencies). We call
this thermal emission ‘black-body’ radiation. The work ‘black’ is used here since the
frequencies emitted have nothing to do with what we see as the color of the body at
ordinary room temperatures. These latter colors are due to particular excitations of
electrons in the atoms and molecules and so depend on what the material is made of.
They can cause special absorption lines, absorption bands, and emission spectra. Such
spectra are very important in identifying materials here or in space.
Thermal radiation from a hot body was extensively studied before 1900 (Kirchhoff,
Wien, Rayleigh, Stefan), but Max Planck was the first to successfully predict the
radiation, using the quantum hypothesis and thus initiating the development of the
quantum theory of matter. His result for the intensity of light emitted per unit wavelength
I 2hc 2 5

 e hc / kT  1
where
h is Planck’s constant (6.62606910-34joule-sec)
c is the speed of light (2.9979108m/sec)
k is Boltzmann’s constant
(1.3806510-23joules/oK).
100
T
0.28978 K cm

max
The total intensity for all
wavelengths (the area under the
curve in the figure) is given by
‘Stefan’s law’ in the form:
T = 6000 K, max=483 nm
80
I (MW/m 2-m)
This ‘Planck distribution’ has a
peak (see figure) which changes as
temperature changes according to
‘Wien’s law’:
60
40
T = 5000 K, max =580 nm
20
I  T 4
where
0
1
 (m)
2
Planck Radiation Intensity Distribution with Wavelength
2 5 k 4
 5.6704  10 8 watts / K 4 m 2 . (If the emitting surface is not ‘perfectly
2 3
15c h
black’, then an additional factor,  , is present, representing the ‘emissivity’ of the
surface.)

Besides the continuous radiation typical of a hot body, certain atoms and molecules will
emit and absorb light at particular frequencies, characteristic of those atoms and
molecules. An example is the dyes used in clothes. For example, a shirt which looks red
might have dyes which absorb green and blue, leaving red to be scattered back to the
observer. Cooler hydrogen and other in the gases around the sun absorbs a set of
particular colors from the continuous radiation emitted by the surface. We detect an
‘absorption spectrum’. Comparing with absorptions of known gases here on Earth, we
can identify elements in the solar atmosphere. Some stars, and hot gases on Earth, will
show an ‘emission spectrum’, with certain bright colors evident. Both absorption and
emission spectra from atoms and molecules in the visible and ultraviolet frequencies are
due to electrons changing quantum states by absorbing or emitting photons.
Procedure:
The following images were made by spreading out the colors of light from various
sources into their colors with a spectroscope. The resulting spectra can often be used to
identify the composition of the source.
3
[If you have a prism of glass, you can also see such colors by looking at the fringe of
some bright object through the prism. A spectrometer confines the light from the object
to a single plane (using a thin rectangular slit), then spreads the colors of that light with a
prism or diffraction grating. A pair of lenses is then used to magnify the image. The
single slit will appear as a band of colors.]
Source #1
Source #2
Source 3
Source #4
Source #5
Source #6
Source #7
1. Identify those which show what appears to be a continuous spectrum, those with
emission spectra lines, those with absorption bands, and those with absorption
spectral lines (these categories not being exclusive).
Extra Credit: The spectra of hydrogen, helium, and calcium are present. Try to find
these spectra in a reference in order to identify these three.
2. Consider the plots of the intensity distributions for light from the bright side of the
Earth, Mars, and Phobos shown below. The lower axis is plotted in wavenumbers
(k), defined by k = 1 / . Note that when I is plotted as a function of k, Wien’s
Law takes on a slightly different form from that given above, becoming
T  (0.510002 K * cm) kmax
where kmax is the wavenumber k when I is maximum. Assume the smooth
curves drawn above the measured intensities are blackbody distributions (with
loss below that curve identifiable as due to gas absorptions), find the peak of the
smooth curves, determine the wavelength of those points, and use Wien’s law to
estimate the radiation temperature of each body.
3. Note the absorption in the spectrum of the Earth’s atmosphere identified by
carbon dioxide (CO2), ozone (O3), and H2O. Which of these three gases shows in
the spectra of the atmosphere of Mars?
A satellite of Mars
(Phobos data from NASA, Mars Orbital Explorer)
_____________________________________
Name
Light Radiation
Answer Sheet
Identification
(if known)
Check:
Check:
Check:
Continuous
Emission
Present
Absorption
Lines or Bands
Present
Emission
Spectra
Present
Source
#1
Source
#2
Source
#3
Source
#4
Source
#5
Source
#6
Source
#7
Wave number at maximum
intensity kmax
Effective Radiation
Temperature of Body
Earth
Mars
Phobos
Likely gases showing in the displayed spectra for the atmosphere of Mars:
CO2
O3
Why do you think Phobos shows no gas absorption?
H2 O