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4. Consider the first overtone vibrational band of the 1'B1ºF molecule within the harmonic oscillator, rigid-rotor approximation. The harmonic vibrational frequency and rotational constant of this isotopomer are equal to 1402.13 cm1 and 1.50724 cm², respectively. Determine the frequency (in cm1) of the J = 5 ->6 R-branch transition in the 1-st overtone. What gives rise to vibrational overtones?

4. Consider the first overtone vibrational band of the 1'B1ºF molecule within the harmonic oscillator, rigid-rotor approximation. The harmonic vibrational frequency and rotational constant of this isotopomer are equal to 1402.13 cm1 and 1.50724 cm², respectively. Determine the frequency (in cm1) of the J = 5 ->6 R-branch transition in the 1-st overtone. What gives rise to vibrational overtones?

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
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4. Consider the first overtone vibrational band of the 1"B1°F molecule within the harmonic oscillator, rigid-rotor approximation. The harmonic vibrational frequency and rotational constant of this isotopomer are equal to 1402.13 cm² and 1.50724 cm², respectively. Determine the frequency (in cm) of the J = 5 > 6 R-branch transition in the 1-st overtone. What gives rise to vibrational overtones? 5. Show that the following are true for hydrogen-like one electron atoms. a) The average value of r for the ground state is 3ao/2Z. b) The most probable value of r for the ground state is ao/Z c) Briefly explain why the above two quantities are different?
Transcribed Image Text:4. Consider the first overtone vibrational band of the 1"B1°F molecule within the harmonic oscillator, rigid-rotor approximation. The harmonic vibrational frequency and rotational constant of this isotopomer are equal to 1402.13 cm² and 1.50724 cm², respectively. Determine the frequency (in cm) of the J = 5 > 6 R-branch transition in the 1-st overtone. What gives rise to vibrational overtones? 5. Show that the following are true for hydrogen-like one electron atoms. a) The average value of r for the ground state is 3ao/2Z. b) The most probable value of r for the ground state is ao/Z c) Briefly explain why the above two quantities are different?
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