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JEE Main202229 Jul 2022Evening ShiftPhysicsKinetic Theory of GasesActual

The root mean square speed of smoke particles of mass 5 × 10 - 17 kg in their Brownian motion in air at NTP is approximately. [Given k = 1 . 38 × 10 - 23 J K - 1 ]

Options

  1. A60   mm   s - 1
  2. B12   mm   s - 1
  3. C15   mm   s - 1
  4. D36   mm   s - 1

Correct answer

C. 15   mm   s - 1

Step-by-step solution

According to Kinetic theory, Average kinetic energy of a gas molecule = 1 2 m v r m s 2 = 3 2 k T Thus, v rms = 3 k T m At NTP, T = 293   K Putting the values, we have = 3 × 1 . 38 × 10 - 23 × 293 5 × 10 - 17 ≈ 15   mm   s - 1

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