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You are using a microscope to view a particle of lycopodium powder suspended in a drop of water on a microscope slide. As water molecules bombard the particle, it "jitters" about in a random motion (Brownian motion). The particle's average kinetic energy is the same as that of a molecule in an ideal gas (K = 3KBT). The particle (assumed to be spherical) has a density of 250 kg/m³ in water at 17°C. (a) If the particle has a diameter d, determine an expression for its rms speed in terms of the diameter d. (Enter your answer as a multiple of d−³/2. Assume Vrms is in m/s and d-3/2 is in m-³/2. Do not include units in your answer.) d-3/2 Vrms= (b) Assuming the particle moves at a constant speed equal to the rms speed, determine the time required for it to travel a distance equal to its diameter. (Enter your answer as a multiple of d5/2. Assume t is in seconds and d5/2 is in m5/2. Do not include units in your answer.) 5/2 t = (c) Evaluate the rms speed (in mm/s) and the time (in ms) required for the particle to travel the distance of one diameter for a particle with a diameter of 4.00 μm. Vrms = t = mm/s ms

You are using a microscope to view a particle of lycopodium powder suspended in a drop of water on a microscope slide. As water molecules bombard the particle, it "jitters" about in a random motion (Brownian motion). The particle's average kinetic energy is the same as that of a molecule in an ideal gas (K = 3KBT). The particle (assumed to be spherical) has a density of 250 kg/m³ in water at 17°C. (a) If the particle has a diameter d, determine an expression for its rms speed in terms of the diameter d. (Enter your answer as a multiple of d−³/2. Assume Vrms is in m/s and d-3/2 is in m-³/2. Do not include units in your answer.) d-3/2 Vrms= (b) Assuming the particle moves at a constant speed equal to the rms speed, determine the time required for it to travel a distance equal to its diameter. (Enter your answer as a multiple of d5/2. Assume t is in seconds and d5/2 is in m5/2. Do not include units in your answer.) 5/2 t = (c) Evaluate the rms speed (in mm/s) and the time (in ms) required for the particle to travel the distance of one diameter for a particle with a diameter of 4.00 μm. Vrms = t = mm/s ms

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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You are using a microscope to view a particle of lycopodium powder suspended in a drop of water on a microscope slide. As water molecules bombard the particle, it "jitters" about in a random motion (Brownian motion). The particle's average kinetic energy is the same as that of a molecule in an ideal gas (K = 3KBT). The particle (assumed to be spherical) has a density of 250 kg/m³ in water at 17ºC. 2 (a) If the particle has a diameter d, determine an expression for its rms speed in terms of the diameter d. (Enter your answer as a multiple of d-³/2. Assume is in m/s and d-3/2 is in m-3/2. Do not include units in your answer.) Vrms d-3/2 Vrms (b) Assuming the particle moves at a constant speed equal to the rms speed, determine the time required for it to travel a distance equal to its diameter. (Enter your answer as a multiple of d5/2. Assume t is in seconds and d5/2 is in m5/2. Do not include units in your answer.) d5/2 t = (c) Evaluate the rms speed (in mm/s) and the time (in ms) required for the particle to travel the distance of one diameter for a particle with a diameter of 4.00 μm. Vrms t = mm/s ms
Transcribed Image Text:You are using a microscope to view a particle of lycopodium powder suspended in a drop of water on a microscope slide. As water molecules bombard the particle, it "jitters" about in a random motion (Brownian motion). The particle's average kinetic energy is the same as that of a molecule in an ideal gas (K = 3KBT). The particle (assumed to be spherical) has a density of 250 kg/m³ in water at 17ºC. 2 (a) If the particle has a diameter d, determine an expression for its rms speed in terms of the diameter d. (Enter your answer as a multiple of d-³/2. Assume is in m/s and d-3/2 is in m-3/2. Do not include units in your answer.) Vrms d-3/2 Vrms (b) Assuming the particle moves at a constant speed equal to the rms speed, determine the time required for it to travel a distance equal to its diameter. (Enter your answer as a multiple of d5/2. Assume t is in seconds and d5/2 is in m5/2. Do not include units in your answer.) d5/2 t = (c) Evaluate the rms speed (in mm/s) and the time (in ms) required for the particle to travel the distance of one diameter for a particle with a diameter of 4.00 μm. Vrms t = mm/s ms
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