This experiment is perfect for Physics 4D as it deals with many topics from our class. We take tubes that contain different gases and raise them to high voltage. This excites the electrons in the gas molecules and creates atomic transitions between the energy levels in the molecules. This creates light at wavelengths that corresponds to the difference between the energy levels. Since the energy levels are distinct, we get light at very specific wavelengths. These wavelengths get diffracted at different angles by the grating in the optical instrument. We can then use the diffraction of the light to identify different elements.

Later in the class we will learn that due to the rules of quantum mechanics, bound states will exist only at certain energy levels. Since electrons are inside the potential well of the atom/molecule, they are in bound states and hence live only at the energy levels possible in the potential well. Since different elements have different nuclei, the electrons in each are exposed to different potential wells and hence exist at different energy levels. When we put energy into a gas (in this case by applying a voltage) we make it easier for electrons to be ejected from the atoms/molecules. When an electron is ejected, another electron will fall down from a higher shell to replace it. When the electron falls into the lower shell, it gives up some energy in the form of a photon. Since there are only a handful of populated energy levels, and since it is the difference in energy levels that determines the energy of the photons, each element/molecule will emit photons with elements characteristic to the element/molecule. Since the energy of the photon is proportional to its frequency, each one of these characteristic photons will also have a known wavelength. By identifying the wavelengths of emitted light, one can identify an element/molecule. We can put some numbers onto this...

The Hydrogen lines in Angstroms have the following wavelengths: 4102, 4340, 4861, 6563

The Hydrogen lines are also known as the Balmer lines, and are produced by Balmer's formula:

λ = B m²/(m²-n²)

Where λ is the wavelength, B is 3646 Angstroms, m is an integer greater than n, and n=2 (n=1 is the Lyman series, 3 is Paschen, 4 is Brackett, 5 is Pfund and 6 is Humphreys).

These wavelengths correspond to an electron falling from the m^th shell down into the n^th shell. In the Bohr model, the energy of a bound electron goes as n^-2, so E₂ = -E/4 whereas E₃= -E/9. The energies are negative because we are discussing a bound system. We will also learn that the energy of light is proportional to its frequency:

E = hf = hc/λ

Therefore the change in energy levels will generate a certain wavelength of light:

hc/λ = E_m-E_n = R(1/n² - 1/m²)

A quick line or two of algebra brings us back to Balmer's formula.

On one end of this experiment we investigate bound energy states, energy being emitted in the form of photons and the relationship between frequency and energy. The other end deals with light as a wave. A grating diffracts the incoming light into different angles. Whereas the idea of light having wavelengths relating to the energy levels in atoms/molecules is a "light as a particle" idea, diffraction is certainly a "light as a wave" concept. Hence we can get both views light. (And when I took photos for this lab, the light hit the CCD in my digital camera, and once again acted as a particle.)

The Experiment:
You will be given a voltage source, a diffraction instrument, and a grating. Start with a Hydrogen tube and use it to calibrate the diffraction instrument. Open the diffraction instrument and place the grating in the center (there should be a clip to help). The grating should be at right angles to the path of the incoming light. On one end of the instrument there will be a small slit. You can adjust the size of this slit with the screw. Start with the slit fairly wide open. On the other end there should be a telescope with crosshairs. Remove it from the instrument and point it at something far away. Adjust it until the crosshairs come into focus. Reassemble the pieces and place the hydrogen tube into the voltage source.

The diffraction grating should go in the middle of the instrument and be perpendicular to the tube with the slit on the end

Turn on the voltage source and watch the gas glow. Line up the diffraction instrument and make sure that at zero degrees you see a nice big bar of color. Once you are sure everything is lined up correctly (and that you can see the crosshairs), close down the slit on the far end of the diffraction instrument so you can make fine measurements. Adjust the position of the telescope in the tube so that both the crosshairs and the line are in focus. You may need to adjust the the positioning of the slit relative to the tube in order to maximize the brightness of the line. Note the angle measurement for the straight-through position and use this as your zero angle.

Find the n=1 diffraction lines for Hydrogen. Write down the angles you find them at and then use those data to determine the spacing of the diffraction grating. It may be useful to also collect second order (n=2) information for H. Always note the color of your lines, this will help in your analysis later. Remember that the formula for diffraction from a grating is:

n λ = d Sin θ

To find d from your data, graph Sin θ on the x axis and λ on the y axis. The slope you obtain should be d. Once you believe you have this as a known, double check this by replacing the Hydrogen tube with a Helium tube and seeing if the Helium lines are where they are predicted to be. Note that the n in this formula is different than the n we had in an earlier equation. This n refers to the order of diffraction, it is not the index for Balmer's formula.

Helium lines in Angstroms - 3889, 4471, 4686. 4922, 5016, 5876, 6678, 7065
Note that you should roughly know what colors these wavelengths correspond to, this should help you in your data fitting.

Here we can see diffraction of the hydrogen spectrum simply by peering through the grating at the light. Both the first order and second order lines are visible here.

A closeup shows four lines from hydrogen. Note that one of the purple lines is very faint, and may be hard to observe by eye (the camera cheats by taking a one-second exposure.)

Once you have Hydrogen and Helium under your belt, start selecting unknown gas tubes and recording at what angles you find them at. Pick either group A, B or C and record data for the four tubes. Some of the tubes have many lines. To identify these, often it is useful to note and record gaps in the spectra, and to write down only the brightest lines. Use the NIST source (http://physics.nist.gov/cgi-bin/AtData/lines_form) to help you identify the unknown gases. Note that you can limit the output to only the strong intensity lines (you will only be able to see those lines). You will be given a selection so that you can narrow your search. Details of how you decided of how each spectra matched a given element are very important and should form the core of your results and discussions section.

Candidates for unknown elements:
Carbon
Oxygen
Nitrogen
Argon
Xenon
Krypton
Gold
Mercury
Neon

In this photo interstellar clouds glow pink, just like your one of your tubes. If an astronomer looked at this spectrum, he or she would find the hydrogen lines, which combine to this color when viewed by our eyes. Since we know exactly where the lines should be, we also know what their frequencies should be. A very important tool in astrophysics is the use of the Doppler effect along with the known frequencies of spectra lines - this tells us how fast an object is moving towards or away from Earth.

NGC 6559