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JEE Main202311 Apr 2023Evening ShiftPhysicsKinetic Theory of GasesActual

The root mean square speed of molecules of nitrogen gas at 27 ° C is approximately: (Given mass of a nitrogen molecule = 4 . 6 × 10 - 26 kg and take Boltzmann constant k B = 1 . 4 × 10 - 23 J K - 1 )

Options

  1. A27 . 4   m   s - 1
  2. B91   m   s - 1
  3. C1260   m   s - 1
  4. D523   m   s - 1

Correct answer

D. 523   m   s - 1

Step-by-step solution

The RMS value of a gas is given by v rms = 3 R T M = 3 k B T m Substituting the given values, v r m s = 3 × 1 . 4 × 10 - 23 × 300 4 . 6 × 10 - 26 ≈ 523   m   s - 1

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