CHEM 301Worksheet #4Particle on a ring andHarmonic oscillator applicationsPart AApplications of particle on a ring1. Referring to the lecture notes for the operator for angular momentum (Lz), calculate theaverage angular momentum for a particle on a ring. The wavefunction for particle on a ringisY( p) =+ im o2n2. Use the particle on a ring model to calculate the wavelength maximum for the indole ring ofthe amino acid Tryptophan, assuming a diameter of 458 p.m.a. Draw an energy diagram for this system. CHEM 301b. Determine the HOMO and LUMO for this system.c. Calculate AE for the HOMO to LUMO transition.d. Calculate the wavelength. Is this what you expected?

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1. Referring to the lecture notes for the operator for angular momentum (Lz), calculate the average angular momentum for a particle on a ring. The wavefunction for particle on a ring is Ψ(φ) = 1 tim, 2n

1. Referring to the lecture notes for the operator for angular momentum (Lz), calculate the average angular momentum for a particle on a ring. The wavefunction for particle on a ring is Ψ(φ) = 1 tim, 2n

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Chapter1: Chemical Foundations

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Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.

Question

CHEM 301
Worksheet #4
Particle on a ring and
Harmonic oscillator applications
Part A
Applications of particle on a ring
1. Referring to the lecture notes for the operator for angular momentum (Lz), calculate the
average angular momentum for a particle on a ring. The wavefunction for particle on a ring
is
Y( p) =
+ im o
2n
2. Use the particle on a ring model to calculate the wavelength maximum for the indole ring of
the amino acid Tryptophan, assuming a diameter of 458 p.m.
a. Draw an energy diagram for this system.

CHEM 301
b. Determine the HOMO and LUMO for this system.
c. Calculate AE for the HOMO to LUMO transition.
d. Calculate the wavelength. Is this what you expected?

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