Chapter 3: Q36E (page 612)

Smoke particles in the air typically have masses of the order of 10^-16 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.

Short Answer

Expert verified

The rms speed of Brownian motion of the particle is $6.44 \times 10^{- 3} m / s$

There is no difference in rms speed for the smoke in air or hydrogen.

Step by step solution

Data and Equation

Given data;

Mass of the smoke particle $m = 3 \times 10^{- 16} k g$

Temperature of smoke particles T = 300K

Boltzmann’s constant $K = 1.361 \times 10^{- 23} J / m o l e K$

Equation;

Rms speed

$V_{r m s} = \sqrt{\frac{3 K T}{M}}$

Find rms speed

Put the all values in equation (1)

$V_{r M S} = \sqrt{\frac{3 (1.381 \times 10^{- 24} J / m o l e K) \times 300 K}{3 \times 10^{- 16} k g}} = 6.44 \times 10^{- 3} m / s$

Hence, the rms speed of Brownian motion of the particle is $6.44 \times 10^{- 3} m / s$ .

Find rms speed of smoke in air and hydrogen

In equation (1) is obtain that rms speed depends on the temperature and the mass of the smoke particles not the type of the surrounding medium. And as the temperature increases the kinetic energy of the smoke particles increase.

Hence, there is no difference in rms speed for the smoke in air or hydrogen.

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Short Answer

Step by step solution

Data and Equation

Find rms speed

Find rms speed of smoke in air and hydrogen

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