Activity 11
Matter/Radiation Interactions
Discussion. In this exercise, you will simulate the transport of radiation from the center of a star
to its surface. You will also simulate the scattering of radiation by atoms and determine the
characteristics of scattered and transmitted light.
What is the nature of light? In the early 1800s, Thomas Young performed his famous double slit
experiment, in which light from a single source was passed through two very narrow, very
closely spaced slits and then projected on a screen. Instead of seeing an image of two slits, Young
saw a pattern of alternating bright and dark bands. He concluded that the light coming through
each slit interfered with the light coming through the other slit, much in the same way that two
sets of concentric circular water waves, each set coming from a separate source, interfered with
one another. By interference, we mean that when two crests of separate waves cross through
each other, they combine to form a larger (but momentary) crest (this is called constructive
interference or reinforcement and when a crest of one wave and a trough of another wave pass
through each other, they cancel each other out (destructive interference or cancellation). From
this experiment and others, scientists of the time concluded that light consisted of a wave.
During the nineteenth century, a number of experiments exposed the link between electricity and
magnetism: under the right conditions, an electric current can generate a magnetic field and a
moving wire passing through a magnetic field can produce an electric current. In 1873, James
Clerk Maxwell published his theory of electromagnetism, which stated (among other things) that
the disturbance of an electric field and its accompanying magnetic field results in
electromagnetic radiation, a wave-like disturbance which travels through space at a speed equal
to the speed of light. In fact, electromagnetic radiation is light (and x-rays, and infrared radiation,
and ultraviolet radiation, and radio and TV waves, etc.). Maxwell's work further strengthened
science's acceptance of the wave theory of light.
In classical wave theory, two measurable properties of a wave are its wavelength, (the Greek
letter lambda), and its frequency, (the Greek letter nu). By wavelength is meant the distance
between a point on a wave to the corresponding point on an adjacent wave. The frequency of a
wave is the number of waves that pass a given point in one second's time. The product of the
wavelength and the frequency is the speed of the wave. For light, c = , where c is the speed of
light in a vacuum. When is expressed in meters and is expressed in sec-1 (reciprocal seconds
or number of waves per second), then c = 3.00 x 108 m/sec.
By the end of the nineteenth century, there was growing evidence that light also displayed
particle behavior (i.e., a beam of light could act as if it were composed of a stream of particles as
well as a number of waves). In 1900, Max Planck concluded that light energy is emitted and
absorbed by matter not continuously, but in discrete "bundles" of energy, which Planck called
quanta (quanta is plural for quantum). From his study, Planck derived a simple equation that 55 related the energy carried by a quantum with the wavelength of the radiation (as measured by
wave theory):
E hc where E is the energy, c is the speed of light in a vacuum, is the wavelength of the radiation,
and h is a constant known as Planck's constant; h = 6.626 x 10-34 J-sec.
Although physicists accepted Planck’s work insofar as it explained a particularly thorny dilemma
that existed at the time regarding radiation of heated bodies, nobody really thought of light's
having particle-like properties until 1905, when Albert Einstein used Planck's quantum theory to
explain the mystery of the photoelectric effect. When light shines on certain metals, it can cause
the metal to eject electrons (this is the basis for "electric eye" doors, light-powered calculators,
motion detectors, etc.). Experiment had shown that only light having frequencies equal to or
greater than a certain threshold frequency (which varies for each metal) would cause the metal to
eject electrons. Einstein interpreted Planck's theory by stating that light consisted of a stream of
particles (dubbed photons). Only those photons having a certain minimum amount of energy
could cause an atom to eject an electron when the atom absorbed the photon. This work, which
won Einstein the Nobel Prize in physics, convinced physicists of the dual nature of light: in
certain experiments, light will display its wave-like nature; in others, light will display its
particle-like nature. Nowadays, this idea does not cause any unwarranted difficulty in a
physicist's mind, but it was quite mind-boggling early in the twentieth century.
Procedure. There are three parts to this experiment.
A. Energy transport. In this part of the exercise, you will simulate the transport of energy from
the center of a star to its surface. As photons leave the center of the star, their progress toward the
surface is not smooth. Photons interact with the atoms and ions of matter it encounters. A photon
is absorbed by an atom or ion and its energy can be re-emitted as a new photon, quite possibly
moving in a different direction from that of the original photon. If you look at successive energy
exchanges by photons, the direction the energy follows becomes a very crooked line, a threedimensional "random walk," as the energy is repeatedly absorbed, reradiated, and scattered on its
way to the surface.
Four classes of interactions between matter and photons describe radiative energy transport, but
the details of these processes will be neglected for purposes of the exercise. As an
oversimplification, let's say that the four processes involve a particle’s (atom, ion, or electron)
absorbing a photon and eventually reradiating energy in the form of a different photon in a
random direction. The direction of photon-flow is random from interaction to interaction.
In Part A of the report sheet, you will find a drawing (Figure 1) of a two-dimensional
representation of a star where each dot represents an atom, ion, or electron. Assume that a photon
is generated at the center dot; you will follow the energy exchanges between the particles in the
star. Further assume that the energy exchanges occur by means of reradiated photons whose
direction is randomly determined. 56 Begin with the center dot. Roll a die to determine in which direction the photon will go. If, for
example, you roll a 2, your photon will move 1 unit diagonally upward to the right (the direction
is determined from the small diagram above the dot representation of a star. At the first dot you
encounter, roll the die again and move 1 unit in the direction specified. Continue doing this until
your photon has completely left the star. CAUTION: When your photon reaches a dot on the
"surface" of the star, you must roll again to determine whether your photon goes in a direction
that moves away from the star or in a direction that sends it back into the star.
As you follow the energy from the center to the surface, mark the path of photons on your
diagram, with pencil and very lightly, and count the number of interactions (rolls) required for
energy generated at the center to leave the surface of the star. Record the total number of rolls on
the report sheet. Repeat this procedure nine more times, for a total of 10 trials. Erase the light
pencil lines before beginning each new trial.
B. Opacity. Atoms exist with only specific distinct energy levels. An atom can jump easily from
one energy level to another by absorbing or emitting energy corresponding to the energy
difference between the two levels involved in the transition. An atom in energy level E2, for
example, can jump to a higher allowed energy level E5 by absorbing a photon of energy E5 - E2;
or an atom can make the transition from E5 to E2 by emitting a photon of energy E5 - E2. Since
the energy of a photon is related to its wavelength, only a specific wavelength will initiate the
transition or result from the transition. In the hydrogen atom, a photon of wavelength = 656 nm
can be absorbed when the hydrogen atom is in its second energy level. This wavelength will
place the hydrogen atom in the third allowed energy level. In about 10-8 second, the hydrogen
atom in the third energy level may spontaneously return to the second level, emitting a photon of
656 nm in the process. This photon goes off in a completely random direction.
In this part of the exercise, you will simulate the interactions between gas atoms and radiation
that can cause energy level transitions in the atoms. Imagine a source of 656 nm photons and a
cloud of hydrogen gas (this cloud could be a nebula near a star or the atmosphere of the star
itself).
Figure 2 on the report sheet is a two-dimensional representation of a cloud of hydrogen gas.
Light from the star enters the cloud from the left and strikes atom #1. Assume that the light
interacts with every atom it encounters. Also make these assumptions: that every hydrogen atom
is in the second energy level and that every photon has a wavelength = 656 nm.
Use a piece of m & m™ candy to represent the photon (when the exercise is finished, you may
eat the candy). When the photon encounters an atom, it is absorbed and soon reradiated, but in a
random direction. At each atom that the photon encounters, roll a die and use the figure in Fig. 2
to establish the direction that the reradiated photon will travel. Continue until the photon leaves
the gas cloud. A photon departing the cloud moving to the right will reach a telescope on Earth.
Try to move 10 photons through the cloud. On the report sheet, record: (1) the number of
photons reaching the telescope; (2) the number of photons not reaching the telescope; (3) the
percentage of photons reaching the telescope; and (4) the percentage not reaching the telescope. 57 C. Scattering of light. In reality, the light entering a gas cloud from a star contains photons of
many different wavelengths. Only photons of certain wavelengths will initiate energy-level
transitions in the atoms they encounter. Photons of other wavelengths are scattered; that is, they
"bounce" off the atoms and travel in new directions.
In this part of the exercise, you will investigate qualitatively what differences arise when photons
of two different wavelengths interact with a gas. Usually, the shorter the wavelength of a photon,
the greater is the probability that it will be scattered.
To simulate what happens when blue-light photons and red-light photons enter a gas cloud, use
Fig. 2 on the report sheet and two dice. Start with a red-light photon (a piece of candy, preferably
a red m & m™) at atom #1. Roll both dice. If you roll 2 or 12, the red-light photon is scattered. If
you roll any other number, the photon keeps moving in its original direction. If the photon is
scattered (you roll 2 or 12), roll one die and use the direction indicator in Fig. 2 to determine the
direction. Repeat this procedure until you have moved 10 red-light photons through the gas
cloud. On the report sheet, record the number of red photons reaching the observer, the number
not reaching the observer, and the percentage of each.
Now do the same for 10 blue-light photons (you may use the same piece of m & m™ candy or a
blue one, if available). Start at atom #1 and roll two dice. If you roll 3, 4, or 5, the blue photon is
scattered; for any other number rolled, the photon continues in the direction that preceded the
encounter with the atom. If the blue photon is scattered, roll one die and determine its new
direction of travel. On the report sheet, record the number of blue photons reaching the observer,
the number not reaching the observer, and the percentage of each.
The phenomenon of scattering of light explains why the daytime sky is blue. Molecules in the air
preferentially scatter blue light more than red. The atmosphere depletes a beam of sunlight (white
light) of its shorter, bluer wavelengths, which are scattered uniformly through the sky. In any
direction you look you see the scattered blue light; thus, the entire daytime sky appears blue.
Light of longer, redder wavelengths reaches you directly along the line of sight. Activity 11 Report Sheet
Matter/Radiation Interactions
A. Energy transport
Use Figure 1 (page 4 of the report sheet) for this part of the activity. Follow the
directions in Activity 11. After each trial, enter the number of rolls of one die
required for a photon to leave the star. 58 Trial 1: Trial 2: Trial 3: Trial 4: Trial 5: Trial 6: Trial 7: Trial 8: Trial 9: Trial 10: Average number of rolls:
A random walk analysis shows that the average number N of rolls required to
move through the distance D of 10 layers in your diagram is D2, or 100 rolls.
1. How does the average number of rolls required in 10 trials compare to the 100
rolls predicted by a random walk analysis?
2. About 1020 interactions occur in getting a photon from the Sun's center to its
surface. If each interaction takes about 108 second, how long does it take (in
years) for a photon to make its way from the Sun's core to its surface? Use 107 for
the number of seconds in one year. B. Opacity Use Figure 2 (page 5 of Report Sheet) for moving the photons through the gas
cloud and answer the following.
Number of photons reaching telescope:
Number of photons not reaching telescope:
Percentage reaching telescope:
Percentage not reaching telescope:
3. Would you describe the hydrogen cloud as being transparent or opaque to
radiation of 656 nm? C. The scattering of light
After using 10 red photons, use 10 blue photons.
59 Number of red photons reaching observer:
Number of red photons not reaching observer:
Percentage of red photons reaching observer:
Percentage of red photons not reaching observer:
Number of blue photons reaching observer:
Number of blue photons not reaching observer:
Percentage of blue photons reaching observer:
Percentage of blue photons not reaching observer:
4. Would you describe this cloud as more or less transparent to the radiation than
in the case in Part B? 5. Has the light reaching the observer been “reddened” or “blued” by the
scattering processes? Sun Atmosphere
Blue light
Red light Blue light
60 Observer Earth's surface Figure 3. The blue sky. Red light passes through the
atmosphere relatively unhindered, but blue light is
scattered in all directions. Because of this, you see a blue sky. 6. Explain why the setting sun appears red. 61 1
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. . 62 Figure 1. Two-dimensional representation of a star. The dots
represent particles. The center of the star is marked by o. 6 1 5 2
4 3 To telescope
on Earth Source of photons
1 Figure 2. To select randomly the direction of reradiation, roll a die
and use the small diagram at the top of the figure. Assume that any
photon leaving the cloud in the “2” direction will reach our telescope
on Earth. Photons leaving the cloud in any other direction do not
reach Earth. 63

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