Sky in a Bottle by Peter Pesic

Author:Peter Pesic [Peter Pesic]
Language: eng
Format: epub
Published: 2009-01-18T16:56:00+00:00

8 Blue Riders

After Rayleigh, the light from the sky could not be understood apart from atomic theory. Connecting the two was part of a many-sided effort to understand how atoms manifest their physical reality. As such, it drew the attention of the young Albert Einstein, who became interested in finding all possible ways of measuring Avogadro's number and hence molecular dimensions from diverse physical and chemical experiments. If this number were always the same, no matter what way it was measured, that would give critical confirmation to the atomic hypothesis. Indeed, by 1909 a dozen different and independent ways of measuring Avogadro's number had all converged on a value between 6 and 9 x 1023.' In the previous chapter, we discussed the way skylight leads to one of these values. But if skylight really depends so deeply on atomic theory, we need to consider further what that theory implies. By considering some of the other ways of finding Avogadro's number, we will be able to return to skylight with a more complete perspective. A strangely varied chain of phenomena will lead us back to sky blue.

Let us begin with Einstein's doctoral work (1905), in which he determined Avogadro's number from the osmosis of sugar solutions. The resulting paper (1906) still remains one of his most cited works, for it proved to be of great practical use in the dairy and construction industries and also in ecology. This may surprise those who think of Einstein as a refined dreamer.' The common link between these oddly diverse activities is the behavior of solutions having suspended particles in various concentrations.

In the 1880s, Jacobus van 't Hoff had discovered osmotic pressure, the force exerted on a semipermeable membrane between two liquid solutions of different concentrations. He formulated an analogy between this pressure and the pressure exerted by a gas, showing that liquids, no less than gases, could be understood by atomic theory. Einstein took up this analogy and, through an ingenious argument, showed how measuring the diffusion and viscosity coefficients of a solution could allow determination of Avogadro's number. From the available data, in 1911 he was able to give a value of NA = 6.6 x 102';.

Only eleven days after he completed his doctoral thesis, Einstein submitted a paper on Brownian motion that led to another way of determining NA. In 1827, Robert Brown had studied the random jiggling of tiny particles he found contained in pollen, observed under a microscope. Gradually, he realized that despite their ceaseless dancing these particles were not living things, and that any particle would dance similarly, if only it were sufficiently small. During the nineteenth century, it became clearer that these motions were the result of the particle being hit by surrounding atoms about 1020 times a second, which often would push it randomly more to one side than the other. Einstein now applied his ideas about solutions to these dancing particles. Again using arguments based on diffusion, he derived a relation connecting the average jiggling of the particle with the viscosity of the surrounding medium and Avogadro's number.

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