Visualization of complex phenomena: Color applet

This applet illustrates the use of a simulation to allow students to focus on different components of a complex phenomenon like why things have color.  (http://ir.chem.cmu.edu/irProject/applets/color/)  We chose this topic because the particle in a box is potentially exciting but this excitement often gets derailed in the mathematics. A complete understanding of this phenomenon requires students to first understand a number of different concepts and then assimilate them into an integrated whole. This is especially true of its use in lecture.  Achieving this goal requires students’ attention to be directed to, for example, how changing the parameters of the particle in a box changes the color absorbed by the material.  This applet is meant for use as a lecture tool before it is used to contextualize homework problems.

Uses in lecture

The following is a sample lecture outline using the color applet:

Light is composed of colors that can be dispersed and recombined with a prism.

A substance that absorbs a certain color appears to have the complementary color. (This may be demonstrated by adjusting the parameters of the particle in the box to get it to absorb the desired color. At this point, no mention of the particle in the box should be made beyond saying that the material is being altered so that it will absorb the desired color.)

The absorbed photons have an energy that corresponds to the spacing between quantum energy levels. The applet may be used while discussing the existence of energy levels. It can also be used to demonstrate that it is the difference between the energy levels that determines the color of light absorbed.

The qualitative aspects of the particle in a box model may then be discussed, focusing on the fact that a particle confined to some region of space will have discrete energy levels. General features of the dependence on mass and length can then be discussed. One suggestion is to create a table on the chalkboard of the spacings that result for some representative lengths and masses. These tables may then be referred to in the later mathematical discussion.

The visible spectrum is a small portion of the electromagnetic spectrum. This can be dem­onstrated using the full spectrum at the top of the applet, and showing that it is only for a small range of box sizes that an electron will absorb visible light.

The previous topic leads nicely into a discussion of what molecular motions lead to absorption in what part of the spectrum. For instance, the idea that an electron has to be in a fairly large box can be used to rationalize why many dyes are conjugated organic molecules. The length of a standard chemical bond can then be discussed and the applet used to demonstrate that an electron in a typical bond absorbs light in the UV. It can then be pointed out that elec­trons are not the only particles that move in a molecule. By putting a particle with a mass of a few amu’s (ex. 5) in a box of a few tenths of an angstrom (ex. 0.3A), it can be shown that molecular vibrations tend to lie in the infrared. Rotations can be discussed as confining the nuclei to a ring with a circumference of 10’s of angstroms, and the applet used to show that such rotations lie in the microwave region. The calculated quantities may be added to the chalkboard table of parameters and calculated quantities started above.

As in the previous stoichiometry applets, this applet enables a fairly thorough and concrete discussion of what phenomena the particle in a box model can be used to explain. Once students know why they should be interested in the model, the mathematics can be discussed on the board. In the above lecture the results  obtained while using the applet were written on the board. These results may now be explicitly calculated while  going back to the applet to remind students why that particular example was of interest.  For instance, if it was calculated to show that electrons in normal bonds absorb light in the UV, then that point can be reinforced and students reminded of the goal of the mathematical calculation.

Uses outside the classroom

The applet can be used both to allow students to answer qualitative questions, and to allow students to check their paper-and-pencil calculations. For instance,

Students can be given the typical size of a nucleus and asked to use the applet to determine the photon energy associated with excitations of the motion of a proton inside a nucleus. This illustrates the wide range of phenomena that can be qualitatively understood with this simple model.

Another suggested qualitative problem is to explain to students that “electrons” in a semicon­ductor have effective masses that differ from that of a real electron. The use of quantum well devices can then be explained and students asked to determine the size of a layer needed to have energy level spacings in the red. A more interesting way to phrase the question is in terms of how many atoms thick a layer would need to be for a quantum-well laser to emit photons in the red.

If students are asked to solve particle in a box questions with paper and pencil, the applet can be used to check their final answers. Note that the applet does not do the work for them. It is roughly equivalent to providing the numerical answer to a practice question, such as is often done at the end of a textbook.