Solution Found!
Smoke particles in the air typically have masses of the
Chapter 18, Problem 40E(choose chapter or problem)
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:
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 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