Calculate the mean free path of a gas molecule, given that the molecular diameter js 2 x 10^–8cm and number of molecules per cc is 3 x 10¹⁹.

Compare the mean free path with mean wavelength of visible light.

Solution

Given,
$Molecular diameter, d = 2 \times 10^{- 8} cm, N u m b e r o f m o l e c u l e s p e r c c, n = 3 \times 10^{19} per cc$

∴
Mean free path of the molecule is given by,

$λ = \frac{1}{\sqrt{2} {πd}^{2} n}$
$= \frac{1}{\sqrt{2} \times 3.14 (2 \times 10^{- 8})^{2} \times 3 \times 10^{19}}$

$= 1.876 \times 10^{- 5} cm = 1.876 \overset{o}{A}$

The average wavelength of visible light is 5800 $\overset{o}{A}$ .

Thus the mean free path is less than the average wavelength of visible light.

Some More Questions From Mechanical Properties of Fluids Chapter

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Mechanical Properties Of Fluids

Calculate the mean free path of a gas molecule, given that the molecular diameter js 2 x 10^–8cm and number of molecules per cc is 3 x 10¹⁹.

Compare the mean free path with mean wavelength of visible light.

Some More Questions From Mechanical Properties of Fluids Chapter

What is sound?

How sound is produced?

Can sound travel in vacuum?

Can two persons hear each other on the moon? Explain.

Can electromagnetic wave propagate in vacuum?

Can we listen in vacuum?

Which of the two moves forward during wave motion - particle or disturbance?

What type of wave is sound wave when it travels in air?

What type of wave is sound wave when it travels in solids?

Which of the two - sound or light is longitudinal in nature?

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NCERT Sample Papers

Entrance Exams Preparation

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Mechanical Properties Of Fluids

Calculate the mean free path of a gas molecule, given that the molecular diameter js 2 x 10–8cm and number of molecules per cc is 3 x 1019. Compare the mean free path with mean wavelength of visible light.

Some More Questions From Mechanical Properties of Fluids Chapter

What is sound?

How sound is produced?

Can sound travel in vacuum?

Can two persons hear each other on the moon? Explain.

Can electromagnetic wave propagate in vacuum?

Can we listen in vacuum?

Which of the two moves forward during wave motion - particle or disturbance?

What type of wave is sound wave when it travels in air?

What type of wave is sound wave when it travels in solids?

Which of the two - sound or light is longitudinal in nature?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Calculate the mean free path of a gas molecule, given that the molecular diameter js 2 x 10^–8cm and number of molecules per cc is 3 x 10¹⁹.

Compare the mean free path with mean wavelength of visible light.