University of Virginia
Physics Department

## Indirect Measurement II

A Physical Science Activity

2003 Virginia SOLs

• PS.1
• PS.3

Objectives

Students will

• conduct controlled experiments;
• record and organize experimental data;
• draw conclusions from collected data;
• describe the Rutherford Gold Foil experiment and its contributions to the development of the Bohr model of the atom;
• explain the importance of using indirect measurement techniques to draw conclusions about objects that cannot be seen;
• estimate the size of the unknown object based on known, comparable dimensions.

Motivation for Learning

Driving Question

How can we measure the characteristics of objects that we cannot see? How do we know the structure of an atom?

Background Information

Often we can look at or touch an object to learn about it. Sometimes, however, objects are too small or too large for us to learn about them this way. When this happens, we need to use indirect measurement techniques. Ernest Rutherford realized that atoms, which are the building blocks of nature, are much too small to be measured directly, and so he designed an experiment to measure their characteristics indirectly. He used a thin piece of gold foil at which he directed alpha particles, which were like very small bullets. Though he could not see the atoms in the gold foil, he knew that if he watched where the alpha particles went after hitting the gold foil, he could draw conclusions about the gold atoms. Alpha particles are very small, but they are heavy. They also travel quickly, and they have a positive electrical charge. When the alpha particles collide with a specially designed screen that Rutherford placed around the gold foil experiment, the screen would light up at the point of the collision.

Imagine a stream of water from a garden hose directed at a brick wall. What would happen to the water as it impacted the wall? Rutherford thought alpha particles against the gold foil would behave much like water against the wall, but he was very surprised to find most of the alpha particles went straight through the foil. Imagine how you would feel if the water from the hose went straight through the wall! This experiment led Rutherford to conclude that an atom is actually mostly empty space with a small, dense, positively charged nucleus in its center.

### Student Activity

Materials

• Small wooden block (approximately 6 inches across) cut into a triangular or circular shape or with irregular edges (must be significantly smaller than the plywood)
• Large piece of plywood (or large, collapsed cardboard box like those in which refrigerators are delivered; foamcore or posterboard could also be substituted) which is much larger than the block and can be placed over the block so that the block cannot be seen (approximately 4'x 6') (Figure 1)
• Marble or steel ball bearing (a ping pong ball or golf ball will also work)
• Supports for the corners of the plywood (spools work well)
• Blackboard or another surface to record data
• Tape
• Hard, level floor

Procedure

1. On a level, hard floor, set up the plywood or large box as shown (Figure 1). Center the wooden block to be used as the "unknown object" under the plywood so it is not visible to the students. (You may want to tape the small block in place so it will not shift when struck with the marble during the experiment.) (Marking off 5 cm increments on all edges of the board will aid in students' identification of exit points.)
2. Have the students form a circle around the plywood. (Figure 2)
3. Draw a sketch of the plywood set-up on the board. Include on it the dimensions of the plywood and the approximate positions of the students around it. You may want to mark the positions on the floor for the students to sit to ensure that they remain properly spaced around the set-up. (Knowing their locations precisely will also increase the accuracy of the experiment.)
4. One student at a time will be the "Launcher" and will roll the marble under the plywood on the floor. An area on one edge should be designated as the "Launch Area" so that all trials start from the same general location. The other students must be ready to catch the marble when it comes out from under the board. The marble should be launched fast enough that it will roll straight through the set-up unless it collides with the center object.
5. Record the path of the marble on a sketch of the set-up on the blackboard. The path should include the exit point from under the plywood and the position within the group of children where the marble was caught. This helps visualize the angle of deflection for the marble. Additionally, point out to the students that the only way for the marble to be deflected is through collision with the small object in the middle. Assume the marble's path is straight line until it collides with the center object. Following the collision, the path is again straight.
6. Students can rotate through the launching position so each has a chance to launch the marble. As students move to the launch position, have other students move around the set-up to ensure each position remains filled.
7. After everyone has rotated through the launch position or after sufficient data are collected, examine the recorded paths followed by the marble. As a group, try to conclude the approximate size and shape of the wooden block.

Recommended "Rules"

1. If the marble collides with one of the supports, do not use the trial. Re-launch the marble.
2. If the marble fails to exit from under the plywood, do not use the trial. Re-launch the marble.
3. When recording the paths of the marble, indicate trials where it collides with the unknown objects differently than those where it does not collide (different colored chalk, for example.)

 Figure 1: Set-up for the activity. The unknown block is placed at the center of the board which is supported at each corner. In this case, rubber stoppers were used. Spools or other small diameter objects will also work. The board has been marked to help students identify the exit point of the marble (shown in the foreground).

 Figure 2: Arrangement of students around experimental set-up

Extensions

1. Students use a computer simulation of Rutherford's Gold Foil experiment (includes programs for Bohr and Schrodinger).
2. Students build a model of the Rutherford gold foil experiment.
3. Students conduct a World Wide Web search for biographical information on Ernest Rutherford.
4. Students compose a newspaper article about Ernest Rutherford and his contributions to the atomic model.

Students with Special Needs

Students unable to participate in the rolling and catching of the marble could serve as data collectors. Or, the participants could be limited to a fraction of the class rather than the entire group while the remainder of the class observes and conjectures on the shape and size of the unknown object.

Click here for further information on laboratories with students with special needs.

Assessment

1. Students identify examples from everyday life where objects are analyzed in a manner similar to the Rutherford Gold Foil experiment.
2. Students place themselves in the position of Ernest Rutherford following his gold foil experiment and write a short paper explaining their feelings about the outcome of the experiment along with their conclusions.