Materials Included In Kit

Additional Materials Required

Safety Precautions

This laboratory activity is not considered hazardous. In the unlikely case of a cracked marble, students should be cautioned not to pick up the glass shards with their hands, but to use the dustpan and brush to pick up the pieces and dispose of them in the proper receptacle.

Disposal

The target sheets may be disposed of in a proper waste receptacle. Marbles may be reused.

Teacher Tips

• Enough materials are provided in this kit for 30 students working in pairs or for 15 teams of students. Both parts of this laboratory activity can reasonably be completed in one 50-minute class period. The data analysis and graphing may be assigned for out-of-class work and the results can be discussed in class the following day.
• Be sure to perform this lab on a smooth, hard floor (e.g., tile, concrete, wood, stone) so the marbles will bounce. Carpeted floors or rough surfaces will not work.
• Encourage students to practice dropping a marble and having their partner catch it after the very first bounce. If marbles are allowed to bounce a second time, the second bounce marks will be fainter, and will not represent the same amount of kinetic energy as the first drops. Make sure that students drop the marbles rather than throw them. The throws usually leave skid marks on the target. For best results, each marble should be dropped from the same height and the same position every time. Sometimes a student may take the easy way out and simply stamp the paper with the marble held in his/her hand. Watch out for an overly regular hit pattern.
• Unless you have plenty of extra marbles available, students should be responsible for returning the marbles at the end of the activity. A few extra marbles (five) are provided in this kit in case some marbles get lost by rolling into inaccessible spaces.

Further Extensions

• Consider having students drop the marble from an even greater height (such as standing on a chair) to illustrate a 3s orbital and to compare the location of the marks made by the marble in the six areas on the target sheet.
• Have each student in the team drop the marble from both waist level and eye level. Students would gather additional data, results would be more accurate if the team averaged their data, and each individual student could do their own data analysis and graphing. The author of this kit, Eve Krupka, suggests that this be done in order to do an individual Performance Assessment.
• In any of these extensions, additional carbonless target sheets are needed. A Quantum Leap Target Sheet Refill Pack (containing 15 waist-level sheets and 15 eye-level sheets) is available, Catalog No. AP6152.
• If time permits, make overhead transparency sheets of the blank Graph Sheet (in the student PDF). Have select groups (or all groups) draw their bar graphs on the transparency sheets using transparency markers. Using the overhead projector, results can then be shared with the class as a whole. Class averages of the data can be determined.

Performance Assessment (Optional)

A Performance Assessment sheet is provided as a Teacher PDF. This sample sheet is provided as an option for use in evaluating the performance of each student. The sheet is meant to be copied in advance and given to the student. The student then performs the lab and completes a lab report, using the Performance Assessment sheet to do a self-evaluation and grading him/herself. The student turns in the lab report with the Assessment sheet attached. The instructor has a blank copy of the Performance Assessment sheet as well. The instructor does a final evaluation on student overall performance and modifies any point values for the total score. 

Performance Assessment is part of the National Science Standards and is considered an essential part to any lab or assignment. The author of this kit, Eve Krupka, has found success with this and suggests doing an individual performance assessment for each student.

Sample Data

The sample data was compiled by averaging many sets of actual student laboratory results. However, student results may vary from the sample data provided.

Target Sheet

Data Table Graph Sheet
Notice that the sample data and graphs for both Waist-Level and Eye-Level targets show that Area 2 received the most hits. Also notice that on the Eye-Level graph, there is a marked decrease in the height of the bars for Areas 1 and 2 while the bar for Area 3 increased appreciatively (as compared to the Waist-Level graph). Even Area 4 received some hits when the marble was dropped from eye level while there were none in this region when dropped from waist level. This can be related to the larger spherical size of the 2s orbital versus the 1s orbital. (Note: This experiment is not meant to be a model for p, d or f orbitals; it is meant to illustrate s orbitals.)

Although the expected outcome is to have the marbles dropped from the waist level hit closer to the center than the ones dropped from the eye level height, in some cases, students get the opposite results. This may be due to an error in mismatching the target sheets, differences in the aiming ability of the students on a team, or improper procedure on the part of the students. In any case, the conclusion should be backed up by the data. Also keep in mind that some students may show less accuracy in dropping the marbles close to the center of the bull’s-eye target and will therefore most likely score hits in all areas. That is why students can be instructed to record hits being made outside Area 5 (labeled as Area 6).

Answers to Questions

1. Which area on each target sheet (Areas 1–6) received the most hits?
   Sample data showed that in both the waist-level and the eye-level cases, Area 2 received the most hits. Actual student data may vary.
2. Why don’t all the marbles dropped from a specified height land in the same spot?
   Many uncertainties alter the landing spot each drop—hand height, horizontal release angle, target movement, etc.
3. As the distance from the nucleus (bull’s-eye) increases, what happens to the probability of finding an electron (marble)?
   The probability peaks in Area 2, and then diminishes, but it never reaches zero.
4. What is the overall shape that the spots made on the target sheet? What differences can be seen between the waist-level target sheet and the eye-level target sheet?
   The overall shape of the spots for each sheet is a circle (or sphere), which is the orbital shape of the s orbital. The difference is that the radius of probability of finding the electron for the eye-level sphere is greater than for the waist-level sphere.
5. Compare the heights of the bars on the waist-level graph and the eye-level graph. Explain the shift in the heights of the bars toward or away from the origin (Area 1).
   There was a shift in the height of the bars for each area away from the origin. In other words, the diameter of the probability circle was smaller when dropped from waist level; the diameter was larger when dropped from eye level.
6. Is there any way to predict the exact location of any one marble drop on the target? Explain.
   No, there is not a way to predict the specific (or exact) place that the marble would land on the target, since both sheets received hits very close to the center and farther away from it. There is, however, a way to predict where the marble would probably hit, since the target sheet demonstrates the probability that any one marble would land in a certain place (i.e., Area 2). Note that the more data points (drops) there are, the more accurate the prediction will be as to where any certain marble would probably land.
7. Describe the relationship between the energy of an electron (drop height), and its probable distance (area number) away from the nucleus of an atom (bull’s-eye).
   As the energy of the marble increases, the further from the center it is likely to fall.

Teacher Handouts

11967_Teacher1.pdf

References

Special thanks to Eve Krupka, Mount St. Mary Academy, Watchung, NJ, for sharing the idea and instructions for this activity. Eve first heard of this activity 11 or 12 years ago at a Woodrow Wilson Institute workshop at SUNY Oneonta, NY. Regretfully, she cannot recall the name of the presenter. The original procedure involved dropping pencils or markers on a target, which Eve did for a few years. The pencils, however, kept breaking and the markers were unusable after the activity. The use of marbles was suggested in the SourceBook and was later compiled in a series of Eisenhower chemistry workshops at the College of New Rochelle in NY by Sr. Mary Virginia Orna, O.S.U.

Orna, M. V.; Schreck, J. O.; Heikkinen, H., eds. SourceBook, Vol. 1 (ATOM), ChemSource, Inc: NY, 1994; pp 8–11, 32–33.

Introduction

Can we know the precise location of an electron around the nucleus of an atom at any given time? This activity will help you to gain an understanding of the concept of probability, and visualize the shapes and relative positions of the 1s and 2s orbitals in a hydrogen atom.

Concepts

• Quantum mechanics
• Electron energy levels
• Heisenberg’s uncertainty principle
• Orbital shapes

Background

Throughout the years, significant progress has been made in our knowledge of the atom. Atoms were originally described by John Dalton (1766–1844), who stated “Thou canst not split an atom!”—revealing the belief at the time that the atom was the smallest particle of matter. Since that time, J. J. Thomson (1856–1940), Ernest Rutherford (1871–1937), and James Chadwick (1891–1974) discovered, in turn, the electron, the proton, and the neutron. The structure of the atom was then described as consisting of electrons orbiting a dense, positively charged nucleus. In turn, Niels Bohr (1885–1962) developed a model for the hydrogen atom in which the electron was assumed to move in definite orbits, called energy levels, about the atomic nucleus. The amount of energy the electron possessed depended on its distance from the nucleus, with the outer orbitals having the most energy. While Bohr’s theory for the structure of the hydrogen atom was very successful, it failed to hold true for atoms with two or more electrons. Hence there was a need for an improved atomic model.

The quantum mechanical model, or quantum mechanics, was developed as a way to describe the motion of small particles (electrons) confined to tiny regions of space. The exact position of an electron at any given instant is not specified; nor is the exact path that the electron takes about the nucleus. Therefore, it is uncertain as to the exact location of the electron at any given time. Heisenberg’s uncertainty principle states that there is a fundamental limitation as to just how precisely both the position and the momentum of a particle can be known at any given time. Quantum mechanics deals only with the probability of finding a particle within a given region of space at any given time. In other words, no longer should we think of definite orbits of electrons around the nucleus (as in the Bohr model). Rather, we should think of regions of space, commonly called orbitals or electron clouds, which represent the most probable location where an electron can be found at any given time around the nucleus, depending on the amount of energy that electron possesses.

In this lab activity, a marble will be dropped repeatedly (100 times) from a specified distance (either waist-level or eye-level) to a bull’s-eye target. The regions of space around the central bull’s-eye will be defined, as shown on the target sheet (Areas 1–6). In each region, there will be a specific probability of locating a spot resulting from the impact of the marble drop. Imagine that each spot represents a point in three-dimensional space around the bull’s-eye (analogous to the nucleus) where the marble (analogous to the electron) is capable of landing (or most likely to be found). The region of space (analogous to an atomic orbital) in which the marble has a high probability of landing will define the shape of the orbital. The maximum probability (as shown by the maximum spot density) will be determined by plotting the number of times the spots appear in each region (analogous to the region of three-dimensional space where an electron is most likely to be observed at any given time).

The activity is repeated at a higher height (eye-level) from the bull’s-eye target. This increased height represents a higher energy level (i.e., 2s orbital) compared to the previous lower energy level (i.e., 1s orbital). The shapes and relative sizes of the 1s and 2s orbitals in an atom can then be illustrated.

(Note: This background provides only a brief overview of the history and development of atomic theory. For additional information, please consult a chemistry textbook.)

Materials

Safety Precautions

This laboratory activity is not considered hazardous. The only consideration would be the unlikely case of a cracked marble. If that happens, do not handle the glass shards with your hands, but use a dustpan and brush to clean up the pieces, and dispose of them properly in the receptacle indicated by the teacher.

Procedure

(Note: Work in teams for the gathering of data. The procedure is written for teams of two; however, it can be easily modified for teams of three, if necessary.)

Waist-Level Target

1. Obtain one waist-level target sheet set for your group and place your names at the top. (Note: Carbonless paper is a special “non-carbon” paper consisting of two attached sheets—one white, one yellow—that make an imprint on the bottom sheet when an object strikes the top sheet.)
2. Choose one person to be the “Target Aimer” and one person to be the “Marble Catcher.” Lay the waist-level target sheet on a smooth, hard floor.
3. The “Target Aimer” should hold a glass marble in one hand and stand over the center of the target. Bend the elbow at the waist so that the forearm is parallel to the floor and perpendicular to the body.
4. Have the “Marble Catcher” kneel down next to the target sheet and be prepared to catch the marble after the first bounce. (Note: Practice bouncing the marble on the floor first to be sure the “Catcher” catches it.)
5. The “Target Aimer” should carefully drop (do not throw!) the marble from waist level, aiming for the bull’s-eye. The “Marble Catcher” should catch the marble after the first bounce to be sure the marble doesn’t leave more than one mark per drop on the target sheet.
6. Repeat this dropping procedure approximately 100 times over the same target. The “Catcher” should make a tally mark after each drop in the Tally Box on the Quantum Leap Data Sheet for ease of counting. Each hit should leave a mark on the bottom yellow sheet. (Note: If three people are in a team, the third person can be the “Tally Marker.”)
7. After 100 drops, carefully separate the bottom yellow sheet from the top white sheet. Notice the pattern of marks on the yellow sheet.

Eye-Level Target

8. Obtain one eye-level target sheet set for your group and place your names at the top. This consists of two attached sheets— one white and one pink.
9. Repeat steps 2–8, with the “Target Aimer” and the “Marble Catcher” switching jobs. This time, use the eye-level target sheets. The “Target Aimer” should drop the marble with the arm fully extended from eye level, aiming for the bull’seye. Try to drop the marble from the same eye-level height each time (100 drops).
10. When done, carefully separate the bottom pink sheet from the top white sheet. Again, notice the pattern of marks on the pink sheet.

Analysis of Data

11. Using a fine-lined pen or pencil, circle each mark made by the marble on both target sheets (yellow waist-level and pink eye-level sheets).
12. Count the number of hits in each target area (1–5) by counting the number of circles. Be sure to also count the hits made outside areas 1–5 as area 6. For those spots that landed exactly on the line between two areas, count it as the lower number.
13. Record all data on the Quantum Leap Data Sheet.
14. Construct a bar graph for each target sheet on the Quantum Leap Graph Sheet. Label the horizontal axis as the area number, and the vertical axis as the number of hits. Space the bars evenly, making each the same width. Draw the height of each bar proportional to the number of hits in that area. The marble dropped from eye level represents an electron having greater energy than one dropped from waist level.
15. Dispose of the top target sheet in a proper waste receptacle. Save the bottom two target sheets as part of your data. Return the marble to your instructor.
16. Answer the Post-Lab Questions.

Student Worksheet PDF

11967_Student1.pdf