
Concept explainers
(a)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In

Answer to Problem 11.22E
The given integral is identically zero.
Explanation of Solution
The wavefunction
The wavefunction
Substitute the value of
The integration of harmonic oscillator is solved using Hermite polynomials. The integral of Hermite polynomials is solved by the formula given in Table 11.2.
In the given integral, the wavefunctions are
The given integral is identically zero.
(b)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In quantum mechanics, the wavefunction is given by

Answer to Problem 11.22E
The given integral is identically zero.
Explanation of Solution
The wavefunction
Substitute the value of
In the above equation,
The given integral is identically zero.
(c)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In quantum mechanics, the wavefunction is given by

Answer to Problem 11.22E
The given integral is not identically zero.
Explanation of Solution
The wavefunction
Substitute the value of
In the above equation,
The given integral is not identically zero.
(d)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In quantum mechanics, the wavefunction is given by

Answer to Problem 11.22E
The given integral is identically zero.
Explanation of Solution
The wavefunction
The wavefunction
Substitute the value of
The integration of harmonic oscillator is solved using Hermite polynomials. The integral of Hermite polynomials is solved by the formula given in Table 11.2.
In the given integral, the wavefunctions are
The given integral is identically zero.
(e)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In quantum mechanics, the wavefunction is given by

Answer to Problem 11.22E
The given integral is not identically zero.
Explanation of Solution
The wavefunction
Substitute the value of
The integration of harmonic oscillator is solved using Hermite polynomials. The integral of Hermite polynomials is solved by the formula given in Table 11.2.
In the given integral, the wavefunctions are
The given integral is not identically zero.
(f)
Interpretation:
Whether the given integrals involving harmonic oscillator wavefunctions is identically zero, not identically zero or indeterminate is to be determined.
Concept introduction:
In quantum mechanics, the wavefunction is given by

Answer to Problem 11.22E
The given integral is indeterminate.
Explanation of Solution
The wavefunction
Substitute the value of
In the above equation,
The given integral is indeterminate.
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Chapter 11 Solutions
PHYSICAL CHEMISTRY-STUDENT SOLN.MAN.
- Problem 6-29 Identify the functional groups in the following molecules, and show the polarity of each: (a) CH3CH2C=N CH, CH, COCH (c) CH3CCH2COCH3 NH2 (e) OCH3 (b) (d) O Problem 6-30 Identify the following reactions as additions, eliminations, substitutions, or rearrangements: (a) CH3CH2Br + NaCN CH3CH2CN ( + NaBr) Acid -OH (+ H2O) catalyst (b) + (c) Heat NO2 Light + 02N-NO2 (+ HNO2) (d)arrow_forwardPredict the organic product of Y that is formed in the reaction below, and draw the skeletal ("line") structures of the missing organic product. Please include all steps & drawings & explanations.arrow_forwardPlease choose the best reagents to complete the following reactionarrow_forward
- Problem 6-17 Look at the following energy diagram: Energy Reaction progress (a) Is AG for the reaction positive or negative? Label it on the diagram. (b) How many steps are involved in the reaction? (c) How many transition states are there? Label them on the diagram. Problem 6-19 What is the difference between a transition state and an intermediate? Problem 6-21 Draw an energy diagram for a two-step reaction with Keq > 1. Label the overall AG°, transition states, and intermediate. Is AG° positive or negative? Problem 6-23 Draw an energy diagram for a reaction with Keq = 1. What is the value of AG° in this reaction?arrow_forwardProblem 6-37 Draw the different monochlorinated constitutional isomers you would obtain by the radical chlorination of the following compounds. (b) (c) Problem 6-39 Show the structure of the carbocation that would result when each of the following alkenes reacts with an acid, H+. (a) (b) (c)arrow_forwardPlease draw the major product of this reaction. Ignore inorganic byproducts and the carboxylic side productarrow_forward
- predict the product formed by the reaction of one mole each of cyclohex-2-en-1-one and lithium diethylcuprate. Assume a hydrolysis step follows the additionarrow_forwardPlease handwriting for questions 1 and 3arrow_forwardIs (CH3)3NHBr an acidic or basic salt? What happens when dissolved in aqueous solution? Doesn't it lose a Br-? Does it interact with the water? Please advise.arrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,Introductory Chemistry: A FoundationChemistryISBN:9781337399425Author:Steven S. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistry: Principles and PracticeChemistryISBN:9780534420123Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward MercerPublisher:Cengage Learning


