Solution Found!
Answer: Smoke particles in the air typically have masses
Chapter 18, Problem 40E(choose chapter or problem)
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.
Questions & Answers
QUESTION:
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.
ANSWER:Solution 40E
Step1 :
We need to find the root mean square speed of the particle
This is given using
Here
We need to find hence rearrange the equation
We get
Substituting the values
Hence the root mean square velocity is obtained as