Statement (I): The mean free path of gas molecules is inversely proportional to square of molecular diameter.

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Q.
Given below are two statements:

Statement (I): The mean free path of gas molecules is inversely proportional to square of molecular diameter.

Statement (II): Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.

In the light of the above statements, choose the correct answer from the options given below: [2024]

1 Statement I is false but Statement II is true

2 Both Statement I and Statement II are true

3 Statement I is true but Statement II is false

4 Both Statement I and Statement II are false

Ans.
(2)

Statement 1: Mean free path

$λ = \frac{1}{\sqrt{2} {πd}^{2} n}$ using $d = 2 r$

   $λ = \frac{1}{4 \sqrt{2} π r^{2} n} \Rightarrow λ \propto \frac{1}{r^{2}}$

  Statement 2:

   $E = \frac{3}{2} k T \Rightarrow E \propto T$

Solution

1 Statement I is false but Statement II is true

2 Both Statement I and Statement II are true

3 Statement I is true but Statement II is false

4 Both Statement I and Statement II are false

Ans.
(2)

Statement 1: Mean free path

$λ = \frac{1}{\sqrt{2} {πd}^{2} n}$ using $d = 2 r$

   $λ = \frac{1}{4 \sqrt{2} π r^{2} n} \Rightarrow λ \propto \frac{1}{r^{2}}$

  Statement 2:

   $E = \frac{3}{2} k T \Rightarrow E \propto T$

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Solution

1 Statement I is false but Statement II is true

2 Both Statement I and Statement II are true

3 Statement I is true but Statement II is false

4 Both Statement I and Statement II are false

Ans. (2) Statement 1: Mean free path λ=12πd2n using d=2r λ=142πr2n⇒λ∝1r2 Statement 2: E=32kT⇒E∝T

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Ans.
(2)

Statement 1: Mean free path

$λ = \frac{1}{\sqrt{2} {πd}^{2} n}$ using $d = 2 r$

$λ = \frac{1}{4 \sqrt{2} π r^{2} n} \Rightarrow λ \propto \frac{1}{r^{2}}$

Statement 2:

$E = \frac{3}{2} k T \Rightarrow E \propto T$