Vibrations in the diatomic molecule CO can be approximated as a harmonic oscillator, where the angular frequencyw = 6.505 x 1013 Hz and the reduced mass is equal to u = 1.14 × 10-27 kg. Assume the molecule is in its fırstexcited vibrational state. Its vibrational wavefunction can then be written as V1 (x) = (4) /2a xe wherea = . If we were to measure the bond length of the molecule, what is the most likely displacement from theequilibrium bond distance in the first excited vibrational state? Give your answer in Angstroms [Note: Theequilibrium displacement in the Quantum harmonic oscillator corresponds to r = 0, ie the coordinate x measuresdisplacement from equilibrium]

The objective of this question is to determine the most likely change of the equilibrium bond…

Vibrations in the diatomic molecule CO can be approximated as a harmonic oscillator, where the angular frequency w = 6.505 x 10¹³ Hz and the reduced mass is equal to μ = 1.14 x 10-27 kg. Assume the molecule is in its first excited vibrational state. Its vibrational wavefunction can then be written as ₁(x) = () ¹ √2α xe¯ √2xxe where ħ α = . If we were to measure the bond length of the molecule, what is the most likely displacement from the equilibrium bond distance in the first excited vibrational state? Give your answer in Angstroms [Note: The equilibrium displacement in the Quantum harmonic oscillator corresponds to x= 0, ie the coordinate a measures displacement from equilibrium]

Vibrations in the diatomic molecule CO can be approximated as a harmonic oscillator, where the angular frequency w = 6.505 x 10¹³ Hz and the reduced mass is equal to μ = 1.14 x 10-27 kg. Assume the molecule is in its first excited vibrational state. Its vibrational wavefunction can then be written as ₁(x) = () ¹ √2α xe¯ √2xxe where ħ α = . If we were to measure the bond length of the molecule, what is the most likely displacement from the equilibrium bond distance in the first excited vibrational state? Give your answer in Angstroms [Note: The equilibrium displacement in the Quantum harmonic oscillator corresponds to x= 0, ie the coordinate a measures displacement from equilibrium]

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Quantum Chemistry

Quantum chemistry deals with the properties of chemical systems and their reactions. The branch of chemistry which is more concerned with quantum chemistry is physical chemistry. It is a more sophisticated field of theoretical physics which is concerned towards the application of physical concepts towards various chemical aspects such as, formation of atoms, chemical structure descriptions, chemical bond strength, hybridization, conjugation etc. Quantum chemistry mainly studies the various states i.e., ground state, excited state, transition states of the individual atoms or molecules taking place during any chemical reaction. The laws of motion explained by various scientists, which are termed as “classical mechanics” were not acceptable in terms of electrons, protons, atoms, light etc. Thus, a new theory named “quantum mechanics” emerged to understand the basic framework of various atomic and subatomic particles.

Question

Vibrations in the diatomic molecule CO can be approximated as a harmonic oscillator, where the angular frequency
w = 6.505 x 1013 Hz and the reduced mass is equal to u = 1.14 × 10-27 kg. Assume the molecule is in its fırst
excited vibrational state. Its vibrational wavefunction can then be written as V1 (x) = (4) /2a xe where
a = . If we were to measure the bond length of the molecule, what is the most likely displacement from the
equilibrium bond distance in the first excited vibrational state? Give your answer in Angstroms [Note: The
equilibrium displacement in the Quantum harmonic oscillator corresponds to r = 0, ie the coordinate x measures
displacement from equilibrium]

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