Carrying out the Activity

1. Tell students that you will now begin to use ball-and-stick models. If students are not familiar with these, you will need to show several simple models to the class.

2. Place on the stage (behind the screen, keeping the model from direct student view) a model of the methane molecule. Turn on the projector. The shadow image on the screen will be a central circle (A) with a somewhat fuzzy circumference surrounded by three rather distinct circles (B). Three lines will connect the four circles. Around the central circle will be a diffuse area of shadow (C) with circumference even more indistinct than its own. It will look something like Figure 1.
   

   Figure 1.

3. Ask students to describe or draw what they think the real model looks like.

4. Turn off the projector before moving the model. Be sure to do this each time you re-position an object.

5. Rotate the model 90º or in some other way that you and your students agree on. You might decide to tell students in advance how you will move each object and then move the object only in the agreed-upon way. The re-positioning should be systematic.

6. In general, the closer “atoms” are to the stage of the projector the more distinct their shadows. Students quickly pick up the idea that “fuzzier” means greater depth (or distance from the projector stage). In the methane molecule there are three planes in the molecule. Three hydrogen atoms are in one plane, the carbon atom in another plane, and the fourth hydrogen atom in the third plane. Careful observation will allow students to correlate planar distance from the projector stage and sharpness of shadow image. The degree of sharpness depends to some extent whether you place the model on the center of the stage or nearer the edge. Additional “depth” can be observed with the models placed closer to the edge than the center. You will need to experiment beforehand with the relative positions of the model, projector, and screen.

7. Continue the re-positioning through all of the agreed upon possibilities.

8. Ask students to draw the “real” model or to make a model that duplicates the one in the activity.

9. Introduce a second, more complex model. If you first used methane, then an ethane model adds a significant level of complexity. You need to know that you can position the ethane model in a number of ways to begin this step.
   1. Rest on the projector the three hydrogens that are connected to one carbon. This means that the model is oriented vertically on the projector, and there are four planes in the shadow.

   2. Rest on the projector four hydrogens, two from each carbon. This produces three planes.

   3. But if you rest one hydrogen from one carbon and two hydrogens from the other carbon, you will have five planes.

   Choose the original position, depending on the complexity you wish to introduce to the activity.

10. Rotate this model in a prescribed manner

11. Continue with as many models or objects as you desire.

Extension

If you use the typical commercially available ball-and-stick models for this activity, you will note that the shadows of “atoms” further from the projector are actually “shadows within shadows” (see Figure 2). That is, there is an umbra and a penumbra to the shadow that gets more pronounced the farther the “atom” is from the projector stage. The difference between the diameter of the umbra and the diameter of the penumbra is a rough measure of the distance between the “atom” in the real model and the stage of the projector. If, then, you want to include a quantitative aspect to this activity, you would ask students to measure on the screen the difference in the two shadows (umbra-penumbra) and use these measurements as a method of indicating which atoms are coplanar in the model. Interested students might be given the task of trying to find an equation for these variables, thus simulating to a greater extent the relationship between this activity and actual X-ray crystallography.

Figure 2.

Summary

Alternative Activity

Relevant National Science Education Standards

Unifying Concepts and Processes — The activity shows how molecular structures can be determined indirectly through skillful interpretation of evidence. The interpretation depends on a good model for the process of X-ray diffraction.

Science as Inquiry — The activity involves inquiry.

Physical Science — The activity is concerned with the structure of matter at the molecular level.

History and Nature of Science — The activity offers historical perspectives that illustrate science as a human endeavor. Also the use of indirect observation to determine molecular structure demonstrates the nature of scientific knowledge.

Relevant New Jersey State Science Education Standards

5.1	The activity involves conducting systematic observations, interpreting and analyzing data, drawing conclusions, and communicating results.
5.2	The activity offers historical perspectives on X-ray crystallography.
5.3	Mathematics can be incorporated into the activity.
5.6	The structure and behavior of matter at the molecular level and at the level of molecular organization are central to the activity.