To study Brownian motion, Bob, a student at the University of Ottawa, used hiscamera to capture the positions (i.e. displacements) of 50 microscopic dustparticles floating on the surface of the water of his aquarium. By setting hiscamera to record 10 frames per second and noting down each particle's 2Ddisplacement for each recorded frame, he managed to obtain the followingmean-displacement vs time graph:1600140012002 1000V80060040020020406080100120140Time (s)a. Use the above mean-displacement graph to roughly approximate thediffusion coefficient D of the dust particles with units of um? /s.b. From the diffusion coefficient estimate in a), calculate the root mean-square displacement expected between each consecutive frame?c. Are the diffusion coefficient D and mean-square displacement calculatedreasonable for a microscopic particle, or did Bob make a mistake in hiscalculations?Mean-square disp. (cm²)

Given, Recording of particles by the camera, u=10frames/s a. The diffusion coefficient=Gradient of…

Answered: To study Brownian motion, Bob, a…

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