Weblecture

# The Nature of Light and Matter: Spectra

## The Dual Nature of Light

### Introduction

Matter emits light when electrons jump between energy levels in atoms. The wavelength or color of the light is precisely determined by the change in energy. Only certain jumps are permitted for an electron in a hydrogen atom; a different set of jumps is permitted for an electron in carbon atoms. This means we can tell what type of atom emitted a particular wavelength of light, and that gives us the composition of our source.

At the moment I am occupied by an investigation with Kirchoff which does not allow us to sleep. Kirchoff has made a totally unexpected discovery, inasmuch as he has found out the cause for the dark lines in the solar spectrum and can produce these lines artificially intensified both in the solar spectrum and in the continuous spectrum of a flame, their position being identical with that of Fraunhofer's lines. Hence the path is opened for the determination of the chemical composition of the Sun and the fixed stars.

— Robert Bunsen, Letter to H. E. Roscoe, November 1859

### Electromagnetic Radiation and how it helps us figure out what is going on in space

#### The particle nature of light

When we look at how light interacts with the matter it strikes, we see evidence of particle-like behavior. Light is the propagation of energy, but the energy delivered is not continuous. It arrives and strikes matter as though it were discrete packets, with the size of the packet dependent on the frequency of the wave:

energy = another constant * frequency

(or to use the wavelength relationship c = λ * ν),

energy = a constant * c / λ.

We call the packets photons.

During the 1800s, the scientists Kirchhoff and Bunsen (of Bunsen-burner fame) showed that different gases produced different spectra, or individual lines of color, when they were heated up. (See the previous lecture for examples of spectra from a household fluorescent lamp). Equally interesting was the phenomena that occurred when a cool gas was placed in front of a hot, full-spectrum light source: dark lines in the spectrum occurred at the same points that the gas produced lines when it was itself heated. Hence a gas when cool has an absorption spectrum and when hot has an emission spectrum that match each other.

It wasn't until discovery of the structure of the atom that scientists were able to explain this. Work by the Marie and Pierre Curie and Henri Becquerel with radioactive materials led to the realization that atoms were not solid, but made up of components. In a series of experiments, James Thompson showed that atoms had a component with a negative charge, the electron. Obviously, then, since most atoms were neutrally charged, there had to be components with a positive charge, and Thompson envisioned his electrons as plums buried in the bread of a positively-charged cloud. Ernst Rutherford's experiments proved this model to be false by showing that the positive charge was concentrated in a very small nucleus. Much later, physical experiments in the 1930's showed that it least some of the mass of the atom was due to neutrally-charged particles, or neutrons.

After Rutherford's experiment, Neils Bohr proposed a planetary model for the orbits of electrons around the positively charged core. The electrical attraction between the positive core and the electron provides the centripetal force to keep the electron in its orbit, and this force in turn establishes a relationship between the velocity of the electron—which is directly related to the electron's energy—and the radius of its orbit. Bohr realized that another condition applied: the circumference of this orbit must equal a integer number of wavelengths of light equal to the electron's kinetic energy.

The result is that an electron can have only specific, discrete, orbits, and not a continuous range of orbits. It will absorb or emit a particular amount of energy or photon, exactly enough energy to change from one acceptable orbit to another acceptable orbit. For an atom with several permissible states, the passage of the electron from a high state to any lower states produces a photon with a different energy amount (and wavelength) for each transition.

 Now we jump back to chapter two and atoms: remember those electrons "circling" the atom at discrete distances? Suppose we want to move an electron from an inner orbital to an outer one. We can't just pump any amount of energy in: the electron needs a specific amount to move outward to the next orbital. Think of seats at the opera: the orchestra seats are $80 a performance, the third balcony rear are$12. The opera sales office will take checks for $80 or for$12, and put in you the right seat. But if you send them a check for \$50, they do not make change: they return the check with a politely-worded letter asking you to remit the correct amount for the seat preferred. In the same way, the electron can absorb or emit a specific amount of energy that will let it jump to a particular energy level and orbital. Having absorbed the energy, when it emits the same amount of energy, it falls back to the original orbital. Now the electron is in a lower, more stable orbit. It can not move to the higher energy level without absorbing energy again. Note that absorbing or emitting energy doesn't change the electron itself; it only changes the electron's energy level, which dictates how fast it moves and how far it can be from the nucleus. So an electron can absorb and emit energy over and over. From light theory, we know that the amount of energy that an electron can absorb corresponds to a given wavelength, which in turn we interpret as a specific color. So we can think of the process this way: the electron absorbs a beam of green light, and jumps up and away from its home atom. In the case of the chemicals in the chloroplast (chlorophylls and carotenoids), the electrons absorb blue and red light. They don't respond to yellow and green light, so those colors are reflected by the cell, and the plant leaf made up of those cells looks green or greenish-yellow to us.

Every element has its own transition emission pattern: one for neutral atoms, more for different ionized states, when it is missing one or more electrons. The patterns for hydrogen atoms have specific names: the Lyman series includes electrons jumping to or from the first energy level, the Balmer series represents electrons jumping to or from the second orbit level, the Paschen series elements jumping to or from the third energy level. Heating the atom raises the number of states that it shows, since a hot atom is one whose electrons have higher energy, and thus can move further out to normally unoccupied orbits.

These patterns act like fingerprints: the spectra from a distant star can thus tell us what elements are present, and how hot the star layer containing the element is.

#### The Doppler shift

There is one other aspect of wave-like behavior that we need to consider. You have all experienced the phenomena where an approaching siren has a high pitch that drops suddenly as the vehicle passes you and recedes into the distance. This is the Doppler shift. It occurs because as the vehicle approaches, each successive wave starts from a position a bit closer to us, so the overall effect is to pack the approaching wavefronts closer together. We experience the sound at a higher frequency than it would have if both we and the source were standing still. As the source moves away from us, each successive wave starts from a position a bit further away, so the wavefronts are further apart, and the overall effect is to decrease the frequency of the sound.

The ratio of the frequency we hear to the frequency emitted is the same as the ratio of the net speed between us and the actual speed of the wave:

For more information on the Doppler shift, including the influence of sonic booms on their environment, check out Daniel Russell's page on the Doppler Effect and Sonic Booms at Kettering University.

You can practice manipulating the values of the source and wavelength by using this simple Java applet on the Doppler Effect. Click anywhere on the grey area and drag in some direction. The more you drag, the faster your velocity vector.

Now play with the Doppler simulator at the University of British Columbia. Scroll down the page until you find "Doppler Effect" and click on it. You can set the source in motion -- see what happens if you have a shortwave source moving in a circle, or if you "bounce" it!

Since this is a general property of waves, we can apply it to light as well as to sound. We can determine the velocity of the source if we know the real wavelength of the light and compare it to the wavelength we observe. How do we know the real wavelength of the light? By looking at the spectral patterns and comparing them to lab patterns where there is no net velocity change between the source and the observer. The Doppler shift, combined with the identification of the actual wavelength using the spectra of elements, allows us to determine the speed at which objects light years away are moving toward or away from Earth.

### Practice with the Concepts

A star's spectral line is observed at 486.3nm when the same line occurs at 486.1 in the lab. How fast is the star moving? In what direction?

### Discussion Questions

• How many different kinds of information can we determine about stars from the light we see coming from them?
• What would happen to our above conclusions if the gravitational constant varied? If energy were not dependent at the same level on wavelength throughout the universe?