Electron Probability Visualizing a Probability Region Chemistry Electron Probability Chemistry MATERIALS beans, pinto cup, 3-oz plastic graduated cylinder, 100 ml meter stick string tape, masking target, custom plastic The picture of an atom that you may have in your mind that of a nucleus with electrons orbiting it like planets around the Sun is outdated and incorrect. We now know that electrons do not travel in orbits but rather simply exist in regions of space around the atoms. The descriptions and shapes of these regions are explained by high-level mathematics and physics concepts that are beyond the scope of this course. However, we can introduce you to some of the basic probability concepts that underlie these mathematical analyses through this simple experiment. Beans will represent an electron and the center of the target will represent the nucleus. Each bean that lands on the target will represent one possible location of an electron. By repeating the drop with 200 electrons, we begin to get a statistical picture of the region where there is the greatest probability that the electron will land. This region of probability is the underlying concept for how we now describe electrons in atoms. The size of the region will be compared for two different drop heights, representing two different energy levels that might be present in an atom. PURPOSE In this activity, you will drop beans on a target and determine the region with the greatest probability of hits. 1
PROCEDURE Work in groups of four. 1. Place the target on the floor and smooth out the wrinkles as much as possible. 2. Fill a graduated cylinder with beans. 3. Use a meter stick to measure a height approximately 0.5 m from the center of the target. 4. Using your hand to cover the top of the cylinder of beans, invert the cylinder so that the opening of the cylinder is at the 0.5 m drop height. Remove your hand and allow the beans to fall onto the target. Repeat with another cylinder of beans if needed until approximately 200 beans are on the target. 5. Position a length of string on the target to make a circle such that approximately 90% of the beans are on the inside of the circle and approximately 10% of the beans are on the outside of the circle. This region represents the area of your target where there is a 90% probability of finding a bean electron. 6. Use the meter stick to measure the average radius of this 90% probability region, and record this value on your student answer page. 7. Count the number of beans that are in each concentric ring on the target and record this value in the data table on your student answer page. Count any beans that landed on a line in the higher numbered area. 8. Repeat Step 4 through Step 7 with a drop height of 1.0 m. 9. When you are finished with both drop heights, clean up your materials as your teacher instructs. 2
DATA AND OBSERVATIONS Radius of 90% probability region: 0.5 m drop height = 1.0 m drop height = Table 1. Data Table Area Number of Beans 0.5 m Drop Height 1.0 m Drop Height 1 2 3 4 5 6 3
ANALYSIS 1. Plot the coordinate points (area number, number of beans) for the 0.5 m drop height on the grid provided. Include (0,0) as one of your points. Draw a smooth curve that connects all of the points. 4
ANALYSIS (CONTINUED) 2. On the same grid, plot the coordinate points for the 1.0 m drop height. Include (0,0) as one of your points. Draw a smooth curve that connects all of the points. 5
CONCLUSION QUESTIONS 1. When dropped from the same height, why don t all of the beans land in the same location? 2. As the distance from the center of the target increases, what happens to the probability of finding a bean? Write a similar statement using the terms nucleus and electron instead of center and bean. 3. Compare the radius of 90% probability for the 0.5 m and 1.0 m drop heights. What conclusion can you draw about the size of the 90% probability region relative to the drop height, or energy level? 4. What shape best approximates the pattern made by the beans on the target? What would this look like in three dimensions rather than two? 6