(Slightly modified McQuarrie 5-41) Many quantum vibrational states are available to molecules. This raises the question: In what vibrational states are molecules actually found? Using sta- tistical mechanics, one can show (see McQuarrie 5-40 if you are interested) that the fraction of molecules in the n-th state is given by: fn = (1-e-hv/kBT) e -nhv/kBT where kB is the Boltzmann constant, kg = 1.380658 × 10-23 J/K. Compute the occupancy of the n=0, 1 and 2 states at 300 K and 1500 K for a "typical" harmonic frequency, we = 2650 cm-1. For practical purposes, what vibrational state is a typical molecule found in?
(Slightly modified McQuarrie 5-41) Many quantum vibrational states are available to molecules. This raises the question: In what vibrational states are molecules actually found? Using sta- tistical mechanics, one can show (see McQuarrie 5-40 if you are interested) that the fraction of molecules in the n-th state is given by: fn = (1-e-hv/kBT) e -nhv/kBT where kB is the Boltzmann constant, kg = 1.380658 × 10-23 J/K. Compute the occupancy of the n=0, 1 and 2 states at 300 K and 1500 K for a "typical" harmonic frequency, we = 2650 cm-1. For practical purposes, what vibrational state is a typical molecule found in?
Physical Chemistry
2nd Edition
ISBN:9781133958437
Author:Ball, David W. (david Warren), BAER, Tomas
Publisher:Ball, David W. (david Warren), BAER, Tomas
Chapter14: Rotational And Vibrational Spectroscopy
Section: Chapter Questions
Problem 14.46E: Determine the number of total degrees of freedom and the number of vibrational degrees of freedom...
Related questions
Question
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Physical Chemistry
Chemistry
ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,
Principles of Modern Chemistry
Chemistry
ISBN:
9781305079113
Author:
David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:
Cengage Learning
Physical Chemistry
Chemistry
ISBN:
9781133958437
Author:
Ball, David W. (david Warren), BAER, Tomas
Publisher:
Wadsworth Cengage Learning,
Principles of Modern Chemistry
Chemistry
ISBN:
9781305079113
Author:
David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:
Cengage Learning