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Consortium for Mathematics and its Applications

Product ID: ILAP
Supplementary Print
Undergraduate
High School

Pollution Police (ILAP)

Author: Jodye I. Selco, Janet L. Beery


Physical Concepts Examined:
1. Molecular vibrations, symmetries, centers of mass, and spectroscopy

Table of Contents:

SETTING THE SCENE

REQUIREMENT 1: CENTER OF MASS AND COORDINATE AXES

REQUIREMENT 2: MOLECULAR VIBRATIONS

REQUIREMENT 3: SYMMETRY ELEMENTS AND SYMMETRY OPERATIONS

REQUIREMENT 4: ORDER OF SYMMETRY OPERATIONS

REQUIREMENT 5: SYMMETRY GROUPS

REQUIREMENT 6: ACTION OF SYMMETRIES ON COORDINATE AXES

REQUIREMENT 7: ACTION OF SYMMETRIES ON VIBRATIONAL MOTIONS

REQUIREMENT 8: COMPARING SYMMETRY OPERATIONS ON AXES AND VIBRATIONS

REQUIREMENT 9: ACTIONS OF SYMMETRIES ON THE xy-PLANE

REQUIREMENT 10: OBTAINING INFRARED SPECTRA

REQUIREMENT 11: IDENTIFYING THE POLLUTANT

REFERENCE

ACKNOWLEDGMENTS

SAMPLE SOLUTION

NOTES FOR THE INSTRUCTOR
Chemical Character Tables
Further Reading

ABOUT THE AUTHORS

©2001 by COMAP, Inc.
Tools for Teaching 2000
35 pages

Mathematics Topics:

Abstract & Linear Algebra

Application Areas:

Physical Sciences , Physical Chemistry (spectroscopy)

Prerequisites:

Matrix representations of linear transformations; Group theory through classifications of groups of small order (up to 12)

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