Probability

Description

Students drop steel spheres onto a target. They measure the resulting distribution of points, and plot those points on a graph.

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Probability concepts are often used in explanations of atomic structure. One can only estimate the probability of finding an electron at particular locations around a nucleus at any given instant. It is impossible to duplicate the conditions inside an atom on a large scale. In this experiment you will study the probability of certain objects coming to rest at given distances from the center of a target. In this manner, you will be better able to understand the use of probability in predicting the location of an electron.

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Use caution about tossing the steel spheres. Handle the inked-paper with caution; the dye causes stains.

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1. Mark the center of a target with a pencil. Turn the target over. Place a mark at the point that corresponds to the center of the bull's eye.
2. Place a square of inked-paper from a ditto master, ink side up, on top of a flat surface.
3. Place the marked target, target side down, on top of the inked-paper so that the center of the target is over the center of the inked-paper.
4. Hold a steel sphere above the target, and drop it from a uniform distance aiming at the small pencil point. Repeat this 100 times.
5.  Spots will be seen on the target.
6. Count the number of spots inside or touching the nearest inner ring. Number the rings from the inside out. Make a plot of the number of spots versus the number of the ring.

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Name _____________________________ Class _______

Teacher______________________________

DoChem 031 Probability

1. On your graph, find the most probable ring from the center of the circle for a sphere to hit. If you dropped the sphere one more time, where would you expect it to hit?
2. Compare your graph with those of other class members. What can you conclude from your comparisons?

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Purpose

To determine the most probable distance from a bull's eye target at which an object will strike when it is dropped toward the target from a fixed distance.

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(10 students in groups of 2)

• 5 target
• 5 ditto master sheet
• 5 steel sphere (0.5 inch steel shot for slingshots works well)
• graph paper

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• Print Figure to use as target.
• Encourage students to develop a technique a uniform drop. If the data do not show enough "spread," ask the students to increase the height from which the sphere is dropped.

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Preparing targets: 20 minutes

Teacher preparation: 5 minutes

Class Time: 30 minutes

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There are no unusual hazards in this experiment.

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Place the inked-paper inside a plastic bag and discard with ordinary trash. Save the steel spheres for future classes.

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Closure questions:

1. On your graph, find the most probable ring from the center of the circle for a sphere to hit. If you dropped the sphere one more time, where would you expect it to hit?
2. Compare your graph with those of other class members. What can you conclude from your comparisons?

Answers to Closure Questions:

1. The most probable ring for the sphere to hit is 3. The next time a sphere is dropped, it could hit anywhere. It is most likely to hit in ring 3, but this only happens about 1 time out of 4.
2. Most graphs show a high concentration of hits in the rings nearest the center, but not in the center. From this you might conclude that most students had about the same skill in sphere-dropping.

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• probability
• distribution
• model for electron probability

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