Since the Schrödinger equation for the particle on a sphere system is solved in the spherical polar coordinate system, the integration must be carried out using the same system. We need to evaluate the integral . If M = 1, then the wavefunction is normalized. Thus, is normalized. Set up an equation for calculating the average value of the Y component of the angular momentum for the system [No need to calculate the integral]. Given the operator for the Y component of the angular momentum , its average value can be calculated as 4. Explain/Illustrate how the rigid rotor model can be applied to the determination of bond length of diatomic molecules. Looking back at the solution to question 1B above, the energy gap between neighboring level of the rigid rotor is , where the momentum of inertia. We also know that the energy gap is related to frequency of the photon by . Thus, we can follow the path to determine the bond length.
Since the Schrödinger equation for the particle on a sphere system is solved in the spherical polar coordinate system, the integration must be carried out using the same system. We need to evaluate the integral . If M = 1, then the wavefunction is normalized. Thus, is normalized. Set up an equation for calculating the average value of the Y component of the angular momentum for the system [No need to calculate the integral]. Given the operator for the Y component of the angular momentum , its average value can be calculated as 4. Explain/Illustrate how the rigid rotor model can be applied to the determination of bond length of diatomic molecules. Looking back at the solution to question 1B above, the energy gap between neighboring level of the rigid rotor is , where the momentum of inertia. We also know that the energy gap is related to frequency of the photon by . Thus, we can follow the path to determine the bond length.
CHEM106-Assessment7-AnswerKey-FINAL.docx