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 theparticle, 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. Assumeis in m/s and d-3/2 is in m-3/2. Do not include units in your answer.)Vrmsd-3/2Vrms(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.)d5/2t =(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 of4.00 μm.Vrmst =mm/sms

Answered: Image /qna-images/answer/9b3c1675-295f-4e1b-93cb-cd2f6cc30341.jpg

Answered: You are using a microscope to view a…

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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An expensive vacuum system can achieve a pressure as low as 1.00 x 10-9 N/m² at 19.5 °C. How many atoms N are there in a cubic centimeter at this pressure and temperature? The Boltzmann constant k = 1.38 x 10-23 J/K. N = atoms
a) Calculate the mean free path in meters of a nitrogen molecule (with a mass m=4.68×10¬26 kg) located in Earth's atmosphere at sea level. Assume a temperature of T=300 K and a number density of particles of 1019 cm-3. b) Assuming that the collision cross-section of the molecule is o = 2x10-10 frequency v in Hertz and the time between collisions t in seconds. m, compute the collision
Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibration mode and have a mass m/4 . The ratio of molar specific heat at constant volume of gas A and B is; a) 7/9 b) 5/9 c) 3/5 d) 5/7
The mean free path is the average distance traveled by a particle between collisions with other particles. Calculate the mean free path of air at room temperature, T = 67.0 °F. Air is mostly nitrogen, so assume that the collisions are between moving N₂ molecules. The diameter of N₂ is d = 1.87 × 10−¹0 m and the gas is at atmospheric pressure, P = 101325 Pa. λ = m
An argon-40 atom has a mass of 6.64 ✕ 10−26 kg. (a) What temperature (in K) would a gas composed entirely of argon-40 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from Earth, 1.12 ✕ 104 m/s? K (b) What temperature (in K) would a gas composed entirely of argon-40 atoms have to be at in order for the rms speed of the atoms to equal the escape speed from the Moon, 2.37 ✕ 103 m/s? K
You are studying a gas known as "gopherine" and looking in the literature you find that someone has reported the partition function for one molecule of this gas, 5/2 AzT q(V, T) = ) %3D h?m Assume that the molecules are independent and indistinguishable. Derive the expressions for the energy, (E), for this gas. Give your answers in terms of N, kg, T. V and the constants A and B. O (E) = NkaT ㅇ (E) =D NkaT ㅇ (E) %3D NkaT- O (E) = ANKET - O (E) = - T ㅇ (E)=D 쑤-
At what temperature would the rms speed of hydrogen atoms equal the following speeds? (Note: The mass of a hydrogen atom is 1.66 x 10-27 kg.) (a) the escape speed from Earth, 1.12 x 104 m/s K (b) the escape speed from the Moon, 2.37 x 10³ m/s K
Suppose that a 1.00 cm' box in the shape of a cube is perfectly evacuated, except for a single particle of mass 1.00 × 10 g. The particle is initially moving perpendic- ular to one of the walls of the box at a speed of 400 m/s. Assume that the collisions of the particle with the walls are elastic. (a) Find the mass density inside the box. (b) Find the average pressure on the walls perpendi- cular to the particle's path. (c) Find the average pressure on the other walls. (d) Find the temperature inside the box. Discuss the as- sumption of elastic collisions, in light of this result.
In interstellar space it is estimated that atomic hydrogen exists at a concentration of one particle per cubic meter. If the collision diameter is 2.5 x 10-10 m, calculate the mean free path 2. The temperature of interstellar space is 2.7 K.
Dr. Chini's research group recently made an interesting discovery, while studying laser interactions with molecular gases. They found that nitrous oxide molecules (mass 44.013 g per mole) can reach temperatures exceeding 745 degrees Celsius after a interacting with a few closely-spaced (in time) laser pulses. At this temperature, what is the rms speed (in m/s) of a nitrous oxide molecule?
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