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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

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

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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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
Transcribed Image Text: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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