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1. Show that the partition function for a harmonic oscillator in the x direction only is given by: 9x exp(-ẞhy) 1-exp(-ẞhv) 2. Using your answer to part (1), derive the partition function for a single harmonic oscillator in three different directions. Briefly note any assumptions made. 3. Using your answer to part (2), show that the partition function for a crystal of n atoms (i.e., a collection of harmonic oscillators in three different directions) is given by: 3N exp(-ẞhv) Qays 1-exp(-ẞhv)

1. Show that the partition function for a harmonic oscillator in the x direction only is given by: 9x exp(-ẞhy) 1-exp(-ẞhv) 2. Using your answer to part (1), derive the partition function for a single harmonic oscillator in three different directions. Briefly note any assumptions made. 3. Using your answer to part (2), show that the partition function for a crystal of n atoms (i.e., a collection of harmonic oscillators in three different directions) is given by: 3N exp(-ẞhv) Qays 1-exp(-ẞhv)

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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1. Show that the partition function for a harmonic oscillator in the x direction only is given by: 9x exp(-ẞhy) 1-exp(-ẞhv) 2. Using your answer to part (1), derive the partition function for a single harmonic oscillator in three different directions. Briefly note any assumptions made. 3. Using your answer to part (2), show that the partition function for a crystal of n atoms (i.e., a collection of harmonic oscillators in three different directions) is given by: 3N exp(-ẞhv) Qays 1-exp(-ẞhv)
Transcribed Image Text:1. Show that the partition function for a harmonic oscillator in the x direction only is given by: 9x exp(-ẞhy) 1-exp(-ẞhv) 2. Using your answer to part (1), derive the partition function for a single harmonic oscillator in three different directions. Briefly note any assumptions made. 3. Using your answer to part (2), show that the partition function for a crystal of n atoms (i.e., a collection of harmonic oscillators in three different directions) is given by: 3N exp(-ẞhv) Qays 1-exp(-ẞhv)
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