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# Smoke particles in the air typically have masses of the ## Problem 40E Chapter 18

University Physics | 13th Edition

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Problem 40E

Smoke particles in the air typically have masses of the order of 10-10 kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with a microscope. (a) Find the root-mean-square speed of Brownian motion for a particle with a mass of 3.00 X 10-16 kg in air at 300 K. (b) Would the root-mean-square speed be different if the particle were in hydrogen gas at the same temperature? Explain.

Step-by-Step Solution:
Step 1 of 2

Solution 40E Step1 : We need to find the root mean square speed of the particle This is given using 1/2m(v ) = 3/2 K × T rms Here 23 K Boltzmann constant = 1.3806 × 10 T absolute temperature = 300 K v root mean square velocity 16 m mass of particle = 3.00 × 10 kg We need to find root mean square velocity hence rearrange the equation We get vrms = 3K×T m Substituting the values 23 vrms = 3×1.380616300 K 3.00×10kg 20 vrms = 1.242160 3.00×10kg 5 vrms = 4.1419 × 10 3 vrms = 6.4357 × 10 m/s = 0.64 cm/s Hence the root mean square velocity is obtained as 0.64 cm/s

Step 2 of 2

##### ISBN: 9780321675460

The full step-by-step solution to problem: 40E from chapter: 18 was answered by Patricia, our top Physics solution expert on 05/06/17, 06:07PM. This full solution covers the following key subjects: air, root, square, speed, Brownian. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The answer to “Smoke particles in the air typically have masses of the order of 10-10 kg. The Brownian motion (rapid, irregular movement) of these particles, resulting from collisions with air molecules, can be observed with a microscope. (a) Find the root-mean-square speed of Brownian motion for a particle with a mass of 3.00 X 10-16 kg in air at 300 K. (b) Would the root-mean-square speed be different if the particle were in hydrogen gas at the same temperature? Explain.” is broken down into a number of easy to follow steps, and 78 words. Since the solution to 40E from 18 chapter was answered, more than 531 students have viewed the full step-by-step answer. University Physics was written by Patricia and is associated to the ISBN: 9780321675460. This textbook survival guide was created for the textbook: University Physics, edition: 13.

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