Communication pubs.acs.org/jchemeduc
Modeling Electron Density and Atomic Orbitals Using Marbles and Carbon Paper: An Exercise for High School Students Zephen Specht*,† and Duke Raley‡ †
Department of Chemistry and Biochemistry, San Diego State University, San Diego, California 92182-1030, United States Science Department, Eastlake High School, 1120 Eastlake Parkway, Chula Vista, California 91915, United States
‡
S Supporting Information *
ABSTRACT: This exercise is designed to teach students about the different types of electron orbitals (specifically s, p, and d orbitals). Electron density and nodes are simulated for each type of orbital by dropping a marble onto a piece of white paper that has been stacked on top of a sheet of carbon paper. The white paper is folded according to specific templates for s, p, or d orbitals. By folding the paper in this manner, certain areas will not be in contact with the carbon paper. These areas remain unmarked as the marble is dropped and illustrate the concept of “nodes” around the “nucleus” of the atom at the center of the paper.
KEYWORDS: High School/Introductory Chemistry, First-Year Undergraduate/General, Physical Chemistry, Hands-On Learning/Manipulatives, Inquiry-Based/Discovery Learning, Atomic Properties/Structure, Nomenclature/Units/Symbols, Student-Centered Learning
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n high school, students are expected to know that electrons are found in clouds, called atomic orbitals, around the nucleus of an atom and that these orbitals form certain patterns that are labeled s, p, d, or f.1 However, the connection between the labels, shapes, and location of the atomic orbitals can be difficult for the students to understand.2 In this exercise, students learn about orbitals and corresponding electron density, the probability of finding the electron around a nucleus, by repeatedly dropping a marble aimed at the center point of a piece of paper stacked on top of a piece of carbon paper. The center point of the paper represents the nucleus of the atom and the marks left on the paper by the marble signify electrons. Previous exercises that have been published are useful for mapping the electron density of an s orbital.3 The exercise presented here allows for the modeling of the electron density and nodes of p and d orbitals by folding the paper according to the templates provided. Different patterns are produced as various folds are made in the paper; unmarked areas represent the space around a nucleus where the electrons are not likely to be found, or nodes, such as in the p and d orbitals.4−7 For this exercise, each student needs three sheets of white paper (the folding patterns for the targets are provided in the Supporting Information), one marble, one sheet of carbon paper, one paper clip, and access to a pair of scissors. This exercise takes between 60 to 75 min to complete for a general or honors high school chemistry class of 20 to 25 students. © XXXX American Chemical Society and Division of Chemical Education, Inc.
UNDERSTANDING ATOMIC ORBITALS
Folding the Target Paper
When introducing the students to the exercise, it is helpful to first demonstrate how to fold the white paper that serves as the canvas for creating the two-dimensional patterns of the threedimensional s, p, and d orbitals. To simplify the folding process, templates are provided for each of three orbital types in the Supporting Information. These pages should be printed on both sides for the students to easily fold along all of the dotted lines. Sheet 1, representing the s orbital, only has a target spot in the center of the page and does not require folding. Sheet 2, the p orbital, should be folded along all three dotted lines, so that a ridge is formed across the center of the page. Sheet 3, the d orbital, is meant to be folded along two perpendicular sets of three dotted lines. To fold the paper properly, with the two ridges intersecting, the paper should first be cut along the solid “I” pattern in the center of the page. Once the paper is cut, the folds form an “X” pattern where the ridges intersect. For sheets 2 and 3, the students will place a paper clip on the ridge at the center of the paper to keep the fold from collapsing during the exercise as well as serving as an easy marker for the “nucleus”. Students Use Marbles To Simulate Electron Density
After the students have prepared their target white papers, they simulate electron density around the nucleus at the center of their paper targets by dropping the marble. A piece of carbon
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dx.doi.org/10.1021/ed400388b | J. Chem. Educ. XXXX, XXX, XXX−XXX
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HAZARDS There are no hazards associated with this laboratory, though students should always be careful when working with scissors.
paper is placed under the sheet of white paper and a marble is dropped from approximately one foot above the paper, aiming for the center, as shown in Figure 1. The marble is dropped 25
CONCLUSION By creating a model of these orbitals themselves, the students gain a greater understanding of the concepts and build a foundation for later topics in chemical reactivy.10,11 The idea of these electron orbitals forming layers around a nucleus will help in understanding concepts such as valence electrons in bonding,12−14 how atoms can absorb and transmit energy and light,15 and why atomic bonds have certain geometries based on the Pauli exclusion principle and valence shell electron pair repulsion (VSEPR) theory.16,17
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ASSOCIATED CONTENT
S Supporting Information *
The template for the three orbitals covered in this exercise, the corresponding worksheet, and the answer key for the worksheet. This material is available free of charge via the Internet at http://pubs.acs.org.
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Figure 1. The student shown is dropping their marble onto sheet 2, aiming for the center of the paper.
AUTHOR INFORMATION
Corresponding Author
*Corresponding Author E-mail:
[email protected].
times to develop a good distribution of points around the center point for sheet 1 (s orbital), 50 times for sheet 2 (p orbital), and 75 times for sheet 3 (d orbital).
Notes
Students Analyze Their Data
The authors declare no competing financial interest.
Once the students are able to conceptualize why the orbitals have a particular shape, it is important for them to make the connection to an orbital’s designated letter (i.e., s, p, d, and f), which is derived from the characteristics of their spectroscopic emission lines on photographic paper: sharp, principal, diffuse, and fundamental.8,9 Included in the Supporting Information is a two-page worksheet to help the students correlate the twodimensional patterns they created in this exercise to the threedimensional diagrams of the different atomic orbitals in their text books, as shown in Figure 2. This worksheet also helps to reinforce other basic ideas about what they have learned in class about the configuration of electron orbitals around the nucleus of an atom.
ACKNOWLEDGMENTS This project was supported by an NSF GK12 fellowship (NSF grant 0742551, Principal Investigator Maarten J. Chrispeels) and the Department of Chemistry and Biochemistry at the University of California San Diego. Jewyl Clark, Melizza Lozano, Timia Crisp, Mallory Hinks, and the students at Eastlake High School were very helpful in developing this project. We would also like to thank Sofia Sandoval and the students at Southwest High School. Special thanks to Nia Ablao, Luis Chavez, Jennifer Chin, Roselle Crisostomo, Alina Corona, Brian Egana, Yoab Garcia, Quincel Quiambao, and Francisco Torres for being photographed as the students performing the exercise.
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REFERENCES
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Figure 2. The students are shown working on their worksheet by comparing what they observed on their target paper and the electron orbital patterns they expected to see. B
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(8) Jue, T. Quantum Mechanic Basic to Biophysical Methods. In Fundamental Concepts in Biophysics; Humana Press: New York, 2009; p 33. (9) Jensen, W. B. The Origin of the s, p, d, and f Orbital Labels. J. Chem. Educ. 2007, 84 (5), 757−758. (10) Tsaparlis, G. Atomic and Molecular Structure in Chemical Education: A Critical Analysis from Various Perspectives of Science Education. J. Chem. Educ. 1997, 74 (8), 922−925. (11) Coll, R. K. Metaphor and Analogy in Science Education: The Role of Models, Mental Models and Analogies in Chemistry Teaching; Springer: Netherlands, 2006; p 65−77. (12) Jensen, W. B. The Origin of the Sigma, Pi, Delta Notation for Chemical Bonds. J. Chem. Educ. 2013, 90 (6), 802−803. (13) Ruddick, K R.; Parrill, A. L.; Petersen, R. L. Introductory Molecular Orbital Theory: An Honors General Chemistry Computational Lab As Implemented Using Three Dimensional Modeling Software. J. Chem. Educ. 2012, 89 (11), 1358−1363. (14) Shusterman, A. J.; Shusterman, G. P. Teaching Chemistry with Electron Density Models. J. Chem. Educ. 1997, 74 (7), 771−776. (15) Hieftje, G. M. Atomic Emission Spectroscopy − It Lasts and Lasts and Lasts. J. Chem. Educ. 2000, 77 (5), 577−583. (16) Cardellini, L. Modeling Chemistry for Effective Chemical Education: An Interview with Ronald J. Gillespie. J. Chem. Educ. 2010, 87 (5), 482−486. (17) Orofino, H.; Faria, R. B. Obtaining the Electron Angular Momentum Coupling Spectroscopic Terms, jj. J. Chem. Educ. 2010, 87 (12), 1451−1454.
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