?This problem is best done using mathematical software. Equation 13B.15 is the partition

Chapter 13, Problem P13B.3

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This problem is best done using mathematical software. Equation 13B.15 is the partition function for a harmonic oscillator. Consider a Morse oscillator (Topic 11C) in which the energy levels are given by

\(E_{v}=\left(v+\frac{1}{2}\right) h c \tilde{v}-\left(v+\frac{1}{2}\right)^{2} h c x_{e} \tilde{v}\)

Evaluate the partition function for this oscillator, remembering to measure energies from the lowest level and to note that there is only a finite number of bound-state levels. Plot the partition function against \(k T / h c \tilde{v}\) for values of \(x_{\mathrm{e}}\) ranging from 0 to 0.1, and-on the same graph-compare your results with that for a harmonic oscillator.

Text Transcription:

E_v=(v+1/2) hc tilde v-(v+1/2)^2 hcx_e tilde v

kT/hc tilde v

x_e

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