Estimating the Sizes of Molecules and Atoms
1. Benjamin Franklin once observed that a teaspoon of oil would spread out over half an acre of lake. Assume for simplicity that the oil molecules are little cubes, what can you conclude about the size of the molecules?
2. From the kinetic theory of gases and the ideal gas law, we deduced a connection between the gas pressure (at some density) and the average molecular speed. We also connected the temperature with the molecular kinetic energy. When Maxwell first analyzed the velocity distribution, he didn't know Boltzmann's constant. Without that knowledge, is there any way the part of kinetic theory we have discussed can be used to guess the size of molecules?
3. By carefully matching Planck's formula for black body radiation to the experimentally observed spectrum, scientists were able to find Avogadro's number, and hence the mass of an atom. Explain. (Assume you already know the gas constant R.)
4. Brownian Motion. Very tiny particles suspended in a fluid are observed to be in incessant motion. Discuss how observation of this motion, together with the principle of equipartition of energy, could lead to an estimate for Avogadro's number.
5. In a J. J. Thomson experiment to measure the ratio of charge to mass for cathode rays -- electrons -- electrons accelerated to a kinetic energy of 3000eV
------------------------------------------------------------------------
....................................................>
------------------------------------------------------------------------
are directed between two metal plates 1 cm apart and 5 cms long, with a voltage difference of 30V . If the beam enters exactly midway between the plates, moving parallel to them initially, how far off center is it as it leaves the plates? If the beam strikes a screen 25 cms beyond the point of exit from the plates, how far off center is the point of impact? If a uniform magnetic field perpendicular to the paper is applied in the region between the plates, what strength and direction is needed to cause the electron path to be a straight line throughout?
French, Special Relativity, Chapter 6: 17, 19