(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In his presentation of the de Broglie wavelength and the wave/particle duality, my quantum prof. has an exercise: "Find the de Broglie wavelength of a molecular vibration. Do quantum or classical laws apply?"

2. Relevant equations

wavelength = h/(momentum)

...

E=h*c*wavenumber*100

...

momentum = Sqrt( 2*reduced mass*E)

3. The attempt at a solution

So, a typical molecular vibration can be dreamed up to be 2100cm^-1 and involve C-triple bond-O stretching (I'm a chemistry student, if you hadn't noticed). This would involve an energy of ~4E-32J. However, if I think about it as a harmonic oscillator, I think that the the center of mass doesn't change, and that the overall momentum must be zero. If I think of it as some sort of very strange particle flying through space with that energy (using the reduced mass), I get a "momentum" of 3E-29 kg*m/s, which gives a de Broglie wavelength of 2E-5 m (and thus can be treated classically). I know that classical treatment is usually used for IR vibrations, and so this result makes sense, but the way I got there definitely doesn't. My prof. mentioned quickly that you can use the uncertainty principle to get at the momentum in the problem, but I'm don't see how that works. Please let me know if this exercise makes sense or not!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: De Broglie wavelength application: molecular vibrations?

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