Problem 6.10. A water molecule can vibrate in various ways, but the easiest type of vibration to excite is the "flexing" mode in which the hydrogen atoms move toward and away from each other but the HO bonds do not stretch. The oscillations of this mode are approximately harmonic, with a frequency of 4.8 x 10¹3 Hz. As for any quantum harmonic oscillator, the energy levels are hf, hf, hf, and so on. None of these levels are degenerate. (a) Calculate the probability of a water molecule being in its flexing ground state and in each of the first two excited states, assuming that it is in equi- librium with a reservoir (say the atmosphere) at 300 K. (Hint: Calculate Z by adding up the first few Boltzmann factors, until the rest are negligible.) (b) Repeat the calculation for a water molecule in equilibrium with a reservoir at 700 K (perhaps in a steam turbine).

Problem 6.10. A water molecule can vibrate in various ways, but the easiest type of vibration to excite is the "flexing" mode in which the hydrogen atoms move toward and away from each other but the HO bonds do not stretch. The oscillations of this mode are approximately harmonic, with a frequency of 4.8 x 10¹3 Hz. As for any quantum harmonic oscillator, the energy levels are hf, hf, hf, and so on. None of these levels are degenerate. (a) Calculate the probability of a water molecule being in its flexing ground state and in each of the first two excited states, assuming that it is in equi- librium with a reservoir (say the atmosphere) at 300 K. (Hint: Calculate Z by adding up the first few Boltzmann factors, until the rest are negligible.) (b) Repeat the calculation for a water molecule in equilibrium with a reservoir at 700 K (perhaps in a steam turbine).

Principles of Modern Chemistry

8th Edition

ISBN:9781305079113

Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler

Chapter4: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 39P: Chapter 3 introduced the concept of a double bond between carbon atoms, represented by C=C , with a...

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