Deduce an expression for the root mean square energy, \(\left\langle\varepsilon^{2}\right\rangle^{1 / 2}\), in terms of the partition function and hence an expression for the root mean square deviation from the mean, \(\Delta \varepsilon=\left(\left\langle\varepsilon^{2}\right\rangle-\langle\varepsilon\rangle^{2}\right)^{1 / 2}\). Evaluate the resulting expression for a harmonic oscillator. Hint: Use \(\left\langle\varepsilon^{2}\right\rangle=(1 / q) \sum_{j} \mathrm{e}^{-\beta \varepsilon_{j}} \varepsilon_{j}^{2}\).

Text Transcription:

langle varepsilon^2 rangle^½

Delta varepsilon=(langle varepsilon^2 rangle-langle varepsilon rangle^2)^1/2}

langle varepsilon^2 rangle=(1/q) sum_j e^-beta varepsilon_j varepsilon_j^2

Chapter 4: Chemical bonding Key: Chemical: chem moles: mol negative: neg molecule: molec Electrons: e different: diff positive: pos Formal Charge: FC Numbers: # threedimensional: 3D Valence electrons: ve With: w/ Gas: (g) structure: struct I. Chemical bonds 3 basic types of chem bonds Ionic: electrostatic attractions between ions Covalent: sharing of e Metallic: metal atoms bonded to one another A. Ionic Compounds Ionic compounds form when a metal cation forms w/ a nonmetal anion 1. Lewis symbols for Ionic Compounds Na (11e): 1s 2s 2p 3s Na (10e): 1s 2s 2p 2 2 6 2 2 6 2 5 2 2 6 2 6 Cl (17e): 1s 2s 2p 3s 3p Cl (18e): 1s 2s 2p 3s 3p 2. Electrostatic Potential Energy Coulombic Attraction Eel= 2.31 x1