A scientist is measuring the random motions of 500 small particles in water at 20°C, in a long, very thin tube. She places all of the particles in a very small point in the middle of the horizontal tube and 30 seconds later, with the aid of a magical camera, she records all of their positions relative to the point of insertion. Arbitrarily, particles to the left of the insertion point are registered as "negative" and those to the right are "positive". She obtains the following table that records the number of particles observed at every approximate displacement. Numbers of particles found at various displacements from the insertion point Number Approximate Displacement, x (um) 1 -400 3 -300 34 -200 109 -100 193 126 100 28 200 300 0. 400 (a) Determine the mean displacement of the particles. Enter your answer in micro-meters. Mean displacement = um (b) Determine the RMS (root-mean-squared) displacement of the particles. Enter your answer in micro-meters. Root mean square displacement = um (c) Determine the diffusion coefficient of these particles. Enter your answer in m/s. Note the dimensionality of the problem! D = m2/s (d) Use the Stokes-Einstein equation to estimate the radius of these quasi-spherical particles. You may need to consult the formula sheet for relevant physical constant/parameters. Give your answer in nanometers. Particle Radius = nm

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Proper Length

The theory of special relativity explains the connection between space and time to objects that move in a straight line at a constant speed. The objects move at the speed of light. When an object approaches light speed, its mass is endless and cannot move faster than light. The most crucial postulate of Einstein's special relativity is that the laws of nature do not change in each frame of reference.