Mastering Physics: Applying the Harmonic Oscillator

The quantum harmonic oscillator is very important in analyzing the spectra of diatomic molecules. It can also be extended to the analysis of polyatomic molecules. In this problem, you will look at how the energy levels of the harmonic oscillator relate to the spectrum of carbon monoxide.

Part A
There is a strong line in the infrared spectrum of carbon monoxide with a wavelength of . What is the energy of a photon in this line?

Express your answer in joules to three significant figures.

ANSWER:	= 4.310×10−20

Part B
It can be shown that this line corresponds to a transition between adjacent energy levels in a harmonic oscillator. If this is true, what is the angular frequency of the oscillator? Use .

Express your answer in inverse seconds to three significant figures.

ANSWER:	= 4.09×1014

Part C
Find the value of , the effective spring constant. Use 16.0 and 12.0 atomic mass units for the masses of oxygen and carbon, respectively. (.)

Express your answer in newtons per meter to two significant figures.

ANSWER:	= 1900

This value is around an order of magnitude smaller than the spring constant for the springs in an average car suspension. Also, this is similar to the effective spring constant for a large trampoline.