**Introduction:** Could we determine the exact position and momentum of a baseball as it soared through the air? Of course we could – by taking a timed series of snapshots of the baseball as it moved. Why can’t scientists follow a similar procedure to determine the position and momentum of an electron?

We can see a moving baseball or its image because of the light bouncing off the baseball. The effect of light on either the position or the momentum of the baseball is negligible. In contrast, an electron has such an extremely small mass that light disturbs its motion in an unpredictable way. How can the position and momentum then be determined for the electron?

Knowledge of the behavior of electrons in the atom comes from theoretical work done in the 1920’s by the German physicist Werner Heisenberg (1901-1976) and Austrian physicist Erwin Schrodinger (1887-1976). Heisenberg postulated that it was impossible to predict the exact position and momentum of an electron simultaneously. This is called the Heisenberg Uncertainty Principle. If you know the position with any precision, then you will know the momentum with less precision, and vice versa. Because of these uncertainties, the exact path that an electron follows cannot be determined. Instead, the quantum-mechanical model for the atom gives the probabilities of finding an electron in a particular region around the nucleus.

In this experiment, we model the probable locations of electrons around the nucleus. We will use dried beans or peas to represent the electrons to help us visualize the regions of low and high density.

**Purpose:** to use dried beans or peas as a model for electrons; to show the probability of electron distribution

**Materials:**

- funnel or cone-shaped paper made into a funnel (with a small opening)
- metric ruler
- pen or pencil
- scissors
- compass for drawing circles
- sheet of large paper (at least 40 cm square- may use newspaper or tape several pieces of paper together)
- dried beans or peas
- plastic container

**Procedure:**

1. Use the compass to draw a circle with a radius of 3 cm in the center of the paper. Then draw four more concentric circles 3 cm apart, around the first circle. Number the rings 1-5, starting from the center. Your circles should look something like this:

2. Mark the center of the innermost circle with a large dot. Let this dot represent the nucleus of the atom.

3. Count out 100 dried beans or peas and place them in a plastic container. Holding the funnel 3 to 4 cm above the paper, add the 100 “electrons” to the funnel. Allow the peas to fall through the funnel onto the paper target. If the peas jam up in the funnel, push them down with a pen or pencil.

4. Count the number of beans in each ring around the nucleus, as well as any that fall outside the rings. Record the data in the table, beginning with the innermost ring.

5. Using the data table, graph the number of peas (vertical or y-axis) vs. the distance from the nucleus (x-axis). A bar graph will work well for this displaying this data. Use Graphical Analysis to create the bar graph by entering data and then clicking on INSERT, then ADDITIONAL GRAPHS, then HISTOGRAM. Right clicking on the histogram (bar graph) will give some additional options for the graph display.

6. Right click on your completed graph and copy it. Paste it into your lab report word processing document in the data section.

**Questions:**

1. Why isn’t it possible to determine the exact path of an electron in an atom?

2. What does the quantum-mechanical model of the atom tell you about the location of an electron in an atom?

3. What do the dried beans or peas represent in this investigation? How did you distribute the beans around the nucleus?

4. What does your graph show you about the probability of finding electrons in particular regions around the nucleus?

5. Can the setup for this experiment be considered a scientific model? Defend your answer.

Completed your lab in the proper lab report format (including data table, graph, and questions answered).

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