HW8 - Physics 3220 Quantum Mechanics 1 Fall 2008 Problem...

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Physics 3220 – Quantum Mechanics 1 – Fall 2008 Problem Set #8 Due Wednesday, Oct 22 at 2pm Problem 8. 1 Review – with some realistic numbers [ 15 pts] A CO (carbon monoxide) molecule can be modeled as a vibrating spring. When you have two objects ("C" and "O" here) it might seem to be a different problem than what we've studied this term, but we will show later this semester that, like in classical physics, you can consider this system to be equivalent to a single object with a reduced mass μ 1/(1/ m 1 +1/ m 2 ) , vibrating like a simple 1-D harmonic oscillator. CO molecules absorb and emit radiation at a wavelength of 47,000 Angstroms. (This is in the IR) This corresponds to excitation (or radiation) of this harmonic oscillator system with a change of the quantum number n=1. Use the above information to deduce the "spring constant", k, between the "C" and "O" atoms in this molecule in MKS units. (M(Carbon)=12 amu, M(Oxygen)=16 amu) (Note that typical, everyday springs have k’s of order 100’s to 1000’s of N/m. Does your “quantum k” surprise you at all?) At room temperature, do you think CO molecules will generally be in their vibrational ground state, or some thermal distribution that would include many excited states? (Why?) Problem 8. 2 Is it a vector? [15 pts]
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HW8 - Physics 3220 Quantum Mechanics 1 Fall 2008 Problem...

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