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JEE Main 202313 AprilEvening Shift
Exam
JEE Main
Year
2023
Date
13 April
Shift
Evening Shift
Subject
Physics
Chapter
Kinetic Theory of Gases

JEE Main 2023 · 13 April · Evening Shift · Physics · Kinetic Theory of Gases

The mean free path of molecules of a certain gas at STP is 1500d ,...

The mean free path of molecules of a certain gas at STP is 1500d1500d, where ddis the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373K373K is approximately:

Options

  1. A750d750d
  2. B1098d1098d
  3. C2049d2049d
  4. D1500d1500d

Correct answer

C. 2049d2049d

Step-by-step solution

The mean free path is given by the relation,

λ=RT2πd2NAP\lambda = \dfrac{RT}{\sqrt{2}\pi{d}^{2}{N}_{A}P}

So, λ∝T\lambda ∝ T

Let λ′\lambda ' be the new mean free path.

Hence,

1500dλ′=273373\dfrac{1500d}{\lambda '} = \dfrac{273}{373}

⇒λ′=2049.45d≈2049d⇒ {\lambda}^{'} = 2049 . 45d \approx 2049d

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