|
|
| Home > JCE Print > Journal of Chemical Education > Issues >
2005
>
May
> |
|
In the Classroom
|
|
|
|
The Pythagorean Theorem and the Solid State
|
Brenda S. Kelly and Allen G. Splittgerber
Department of Chemistry, Gustavus Adolphus College, Saint Peter, MN 56082-1498
|
|
May 2005
Vol. 82 No. 5
p. 756
|
|
|
|
|
|
|
| Abstract |
|
Solid-state parameters such as radius ratios, packing efficiencies, and crystal densities may be calculated for various crystal structures from basic Euclidean geometry relating to the Pythagorean theorem of right triangles. Because simpler cases are often discussed in the standard inorganic chemistry texts, this article only presents calculations for closest-packed A-type lattices (one type of particle) and several compound AB lattices (A and B particles) including sodium chloride, cesium chloride, zinc blende (sphalerite), wurtzite, and fluorite. For A-type metallic crystals, the use of recommended values of atomic radii results in calculated densities within 1% of observed values. For AB lattices, assuming ionic crystals, the use of recommended values of ionic radii results in density determinations that are usually but not always close to observed values. When there is covalent character to the bonding, the use of covalent radii results in calculated densities that correlate well with observed values. If interionic or interatomic spacings are used, the calculated densities are always close to the observed values. As indicated by a survey of the standard inorganic texts, these calculations are generally not presented. However, as an illustration of the application of simple mathematical principles to the study of chemistry, discussion of the methods presented in this manuscript may be of value in classroom presentations pertaining to the solid state.
|
|
| More Information |
 Citation |
Kelly, Brenda S.; Splittgerber, Allen G. J. Chem. Educ. 2005 82 756.
|
Keywords |
Crystallography / Crystal Growth; Inorganic Chemistry; Solid-State Chemistry
|
History |
Created:
Last Updated: |
March 28, 2005
April 15, 2005
|
|
|
|
|
|
| Home > JCE Print > Journal of Chemical Education > Issues >
2005
>
May
> Page
756
|
|
|
| Chemistry Teacher Connection |
|
The "Chemistry Teacher Connection" (CTC) is especially for high school chemistry teachers. For only $40/year, it offers an online-only subscription to CLIC along with membership in the Division of Chemical Education, normally $65/year. CTC subscribers receive access to all articles and supplements from 1996 through the current issue.
|
| C&EN CLICs |
|
Through special arrangement with the ACS, JCE High School CLIC is now able to provide subscribers with online access to Chemical & Engineering News articles that have been selected specifically for secondary science instructors and their students.
|
JCE Collections Available
|
Occasionally, collections of JCE back issues become available for donation to individual teachers, schools, or libraries. JCE matches collections with interested recipients. Recipients pay shipping costs or pick up the collection.
|
| Contributions Welcome |
| JCE welcomes your submission |
| Fishing for New Ideas |
 Always in the
process of
improving, CLIC
welcomes ideas and comments.
Email Us |
|
