Models of the Hydrogen Atom

1. Distinguish between several models of the hydrogen atom visually and conceptually.
2. Compare and contrast the accuracy and usefulness (including the shortcomings) of various models of the hydrogen atom.
3. Relate spectrometer outputs and transitions represented on energy level diagrams to observed phenomena of the hydrogen atom.

• Educational level: High School/Undergraduate/Upper Level Physics
• Setting: Modern Physics or Chemistry Class lecture
• Time required: 40+ minutes
• Special equipment: Internet/Java capable computer, digital projector
• Pre-requisite knowledge: EM spectrum, Rutherford's model of the atom

1. Open the Java applet Hydrogen Atom Model Applet.
2. Run the default simulation experiment by pressing the "on" button of the light source (which is a red button on the ray gun).
3. As the simulation runs, a few things should be pointed out to the students:
1. The different colored dots represent different colored light. The size and shape of the dots are not important, only the color.
2. The big question mark represents a hydrogen atom. We know that it's hydrogen; it's the internal structure and the mechanisms for causing observed phenomena that we're unsure of.
3. You should have noticed by now that what goes in the "?" is not what always comes out. We can keep track of what's emitted by setting up a spectrometer to record emitted light. This is precisely what has been done in laboratory settings.
4. Check the "Show spectrometer" box to activate the spectrometer. Demonstrate that counts of emitted light increase as interactions occur.
5. Ask the following Guiding Question:
   "Imagine you're new to physics and discussion of the atom has begun. What is the simplest model of an atom you can think of?"
   Students may suggest an array of models, but lead them to the simplest model: a rigid billiard ball. Encourage students to think of the simplest possible model first--hold up a ball if necessary to generate ideas.
6. Select the Billiard Ball model and have students report back whether they think it accurately represents what's been observed in laboratory settings.
7. Going in order from top to bottom, select the different models and allow time for students to observe interactions as predicted by each. For each model selected, have students work in pairs to write down their impressions of how accurately the model predicts the actual behavior.
   The theme that should present itself is that as the models get greater predictive power, they also get more complicated and less intuitive.
   Promting questions:
   • How is the overall appearance of the model different from the other(s) just seen?
   • Can you notice any differences in the interactions with incident light?
   • How do these models compare with other commonly known models? (i.e. rigid object of the Newtonian world, solar system like appearance, orbits, etc.)

1. Turn the spectrometer on and active the energy level diagram.
2. With these two features displaying simultaneously, have students record information down as you hit the "pause" button every so often.
3. As a class, use the data collected by students to find patterns among transitions between multiple energy levels, photon energy, quantum numbers, and energy released/absorbed as a function of quantum state changes.
   A nice feature of this applet is that visual representations of what happens to the electron are well-depicted simultaneously with energy level changes and spectrometer output.
4. At this point, student questions should guide further discussion. If students aren't asking questions, have them come up with a question as a think-pair-share exercise.

Promting questions:
• Does something always happen? What role does chance or probability play for interactions?
• This model is for the hydrogen atom. How do you think things might change for more massive atoms?
• What are some shortcomings of these models?

This is the spectrograph output for a 10 minute run on "fast" in experiment mode.

This is the spectrograph output for a 10 minute run on "fast" for the Bohr model.

This is the spectrograph output for a 10 minute run on "fast" for the deBroglie model.

This is the spectrograph output for a 10 minute run on "fast" for the Schrödinger model.

A PowerPoint file including all of the model spectrograph images alongside the experimental output has been created for convenience: Spectrograph Outputs (PowerPoint 68kB Jul24 07).

General:
It is highly advised to spend time familiarizing yourself with the applet prior to use in class. Although the applet is easy to use, it has several features that may lead you to modifying its use during class and for developing assignments.

This applet could easily be used to supplement example numerical problems. The provided example evaluation/assessment below is a mix of qualitative and quantitative problems. Depending on the level of your students and course goals, this activity could be expanded to accommodate an upper level modern physics class.

Other Important Information:

• Be advised that this applet is still in the testing phase as outlined by PhET.
• If interactions with incident light cease, click on the mock bakelight switch to restart the simulation.
• If during class time you wish to collect ample data on the spectrometer for comparisons, increase the speed of the applet to "fast" at the bottom of the window. This is also recommended for students if they are to complete an assignment comparing spectrometer outputs.
• For the deBroglie model, there are alternative views selectable from a drop down menu at the top of the applet.
• The main window of the applet displays possible quantum numbers as the atom changes state. However, m = -1 is not shown as a possibility. This value for m is shown in the energy level diagram as it occurs.

• This applet is managed by the Physics Education Technology program at the University of Colorado at Boulder.
• The full url for the applet is http://phet.colorado.edu/simulations/hydrogen-atom/hydrogen-atom.jnlp.
• One question in the sample assessment questions is taken from Randall D. Knight's Physics for Scientists and Engineers with Modern Physics, 2004.
• Related published article: S. B. McKagan, K. K. Perkins, and C. E. Wieman, "Why we should teach the Bohr model and how to teach it effectively," submitted to Physical Review Special Topics: PER.