Wednesday, May 12, 2010

Do atoms behave as waves?

As you may recall, I was recently banned for life from the discussion group However, from time to time discussions take place in which I would like to put in my two cents worth. Today I am going to comment on the thread "Do atoms behave as waves?".

The most compelling evidence of atoms behaving as waves is the anomalous specific heat of diatomic gasses, which was known in the nineteenth century and caused great concern for people like Maxwell and Boltzmann. Here is the problem: the thermal energy of the typical diatomic gas such oxygen, nitrogen, or hydrogen is classically accounted for by counting the five modes: three translational and two rotational. (The third rotational mode contributes no energy because it is oriented along the axis of the dumbbell.) The theory works well in practise, except at low temperatures hydrogen begins to diverge from the expected value. It's as though the rotational modes stop contributing and only the translational modes remain in effect.

This is a clear instance of the wave nature of atoms. In order to properly drive the rotational modes, the dumbbell has to be cleanly struck by another atom. With classical billiard balls connected by pegs, this is no problem. But since atoms behave as waves, it's not so simple. At lower temperatures, the atoms move slower, so the wavelength gets longer. At a certain point, the wavelenght of the molecule is longer than the length of the dumbell, so it is impossible to strike one atom without also striking the other one as well. Therefore it is impossible to set the molecule in rotation to the full extent which is possible with simple billiard balls on pegs.

If you do the simple calculation of de Broglie wavelengths at the mean molecular speed and set it equal to bond length of the molecule, you get (within an order of magnitude) the well-known classical Wien formula for peak radiation frequency at a given temperature. It is interesting that you can get this result without recourse to the assumption that energy is quantized in lumps.

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