Problem sets for Prelude

Problem Pr.l On average, how far apart are molecules in a dilute gas Show that, for a gas at 1-atm pressure at room temperature, the average interparticle distance is —30 A. 

Problem Pr.2 Calculate the effective Hamaker coefficient between the spherical atom and the gold surface. 

Problem Pr.3 Show that the interaction between spheres separated by distances much greater than their radii will always be much less than thermal energy kT. 

Solution This weakness of inverse-sixth-power van der Waals forces between small particles is discussed at length in the main text. Its thermal triviality is easily seen. Begin with [—(16/9)](R6/z6)AHam for the energy of interaction between two spheres of radius R and center-to-center separation z and ask what the Ah am would have to be for the magnitude of this energy to be comparable with kT, (16/9)(R6/z6)AHam = kT or Anam = (9/16)(z6/R6)kT. Even if the center-to-center separation z were equal to 4R, spheres separated by a distance equal to their diameter, R6/z6 would be 46 = 4096. Anam would have to be a ridiculous 4096 x (9/16) kT = 2304 kT for there to be thermally significant attraction. 

Problem Pr.4 Try something harder than spheres. Consider parallel cylinders of radius R, fixed length L, and surface separation Z. Use the tabulated energy per unit length 

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