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Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437

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Section
BuyFindarrow_forward

Physical Chemistry

2nd Edition
Ball + 3 others
Publisher: Wadsworth Cengage Learning,
ISBN: 9781133958437
Chapter 11, Problem 11.87E
Textbook Problem
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Evaluate L z for 3 p x , Compare it to the answer in Example 11.25, and explain the difference in the answers.

Interpretation Introduction

Interpretation:

The Lz for 3px is to be stated and the answer is to be compared with Example 11.25.

Concept introduction:

The wavefunction for 3-D rotational motion involves spherical polar coordinates to explain the motion in three dimensions. It is given by the expression as follows.

Ψm,l=12πeimϕθl,ml

Where, Ψmrepresents the wavefunction dependent on quantum number m and l. The values of m and l start from 0. Also, they can take up both negative and positive integral values. According to Euler’s identity, eimϕ can be written as cosϕ+isinϕ.

Explanation of Solution

The wavefunction 3px can be written as follows.

3px=12(Ψ3p+1+Ψ3p1)Ψ3px=181(2πa3)1/2(6rar2a2)er/2asinθcosϕ

The value of Lz can be calculated as follows.

002π0πΨ3px*LzΨ3pxdτ=i812πa3002π0π(6rar2a2)2e2r/3asin3θcos

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Chapter 11 Solutions

Physical Chemistry
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Ch. 11 - Derive equation 11.16 from the equation...Ch. 11 - Show that the energy separation between any two...Ch. 11 - a For a pendulum having classical frequency of...Ch. 11 - a A hydrogen atom bonded to a surface is acting as...Ch. 11 - The OH bond in water vibrates at a frequency of...Ch. 11 - Show that 2 and 3 for the harmonic oscillator are...Ch. 11 - Substitute 1 into the complete expression for the...Ch. 11 - Demonstrate that x=0 for any wavefunction of a...Ch. 11 - Calculate px for 0 and 1 for a harmonic...Ch. 11 - Use the expression for 1 in equations 11.17 and...Ch. 11 - Derive equation 11.19 from the information in...Ch. 11 - Simply using arguments based on odd or even...Ch. 11 - Consider Figure 11.4 and choose the correct...Ch. 11 - Based on the trend shown in Figure 11.5, draw the...Ch. 11 - What is x2 for 0 of a harmonic oscillator? 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