Problem Set 8 - Quantum Mechanics I - Fall 2009 | PHY 389K, Assignments of Quantum Mechanics

Download Problem Set 8 - Quantum Mechanics I - Fall 2009 | PHY 389K and more Assignments Quantum Mechanics in PDF only on Docsity! PHY 389K Homework 8 9 April 2009 Page 1 of 2 Problem 1: The experimental values for the emitted radiation in the far infrared region for the HCl molecule are given in the following table. jo72-y [Hz] | 2.49 3.12 3.74 436 497 5.58 for £ 4 5 6 7 8 9 a) Determine the value of the moment of inertia for the dumbbell of the HC] molecule in its vibrational ground state. b) Calculate the energy values in eV and in J (joules) for the 1st, 2nd, 3rd, 4th, and 5th energy levels above the ground state level. c) Calculate the “size” of the HCl molecule (the length of the dumbbell axis) using the result of Problem la and the masses of the H and Cl atoms. d) Take into consideration that the HCl molecule is not only a rigid rotator but can also perform vibrations along its internuclear axis. Its Hamiltonian is therefore given by FH = Hose @1+1® yor + 9Hose @ Hyot; where 1 Hose = fiw(N + 3) is the oscillator Hamiltonian, a= a” is the rotator Hamiltonian, e and the third term in H describes the interaction between rota- tions and vibrations. Considering selection rules for dipole ra- diation, calculate the energy spectrum of the vibrating rotator, ignoring the fact that the moment of inertia could change due to the vibrations.