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

Chem 142: Week 7: Lectures 4.1-4.4 Chapters (4.1-.6, 4.8, 4.9-.12) Key and Introduction: If you see text in this purple color, it just means that I have added side notes that I thought were significant from the textbook reading. (exclude the purple that I have used on page 5) Words in bold are important vocab words included for this week My note summaries are all based off of lectures and textbook readings. I will upload notes once every week summarizing notes, lectures, and textbook readings from class. Each week will have a different theme to make these notes a bit more colorful. I hope you enjoy these notes!!! If there are anything that you think would help my notes to become more beneficial, please leave comments below my post. Thank you. Lecture 4.1 Aqueous solution: water based solution Water A “bent” molecule (polar) Asymmetric: Partial () charge on Oxygen and Partial (+) charge on Hydrogen Electron density: red elevated (high) areas & blue reduced (low) areas Solution Formation Solution: Mixture of solvent (the one that does the dissolving) and solute (substance being dissolved) When dissolved in water… Ionic compound Molecular com