In one of his experiments on gravitational sedimentation, Perrin is observing se

Question

In one of his experiments on gravitational sedimentation, Perrin is observing sedimentary particles in water at T-293K. He finds that when his microscope is raised 100 micromeres higher up the cross section of his water sample, the mean number of particles in the field of view decreases from 203 to 91 (the size of field of view does not change but rather his microscope is horizontally observing the water and is moved up in the z direction). If the molar gas constant is R = 8, 32 J.K^-1, calculate Avogadro's number using the observations above. Assume that each particle has a mean volume of_9,78 Times 10^-21 m^3, and a density of 1351 kg.m^-3. The density of water is 1000 kg.m^-3. Assume that you do not know value of the Boltzmann constant.

Explanation / Answer

Here, Net Force = mg - Archimedes Force

=>   Net Force =      9.78 * 10-21 * 9.81 * (1351 - 1000)

                           =   3.367 * 10-17 N

=>    E =   3.367 * 10-17 * 100 * 10-6 J

             =   3.367 * 10-21   J

=>    Avogadro's number = (293 * 8.314 * )/(1.12 * 3.367 * 10-21 )

                                          = 6.45 * 1023

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