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JEE Main20198 Apr 2019Evening ShiftPhysicsKinetic Theory of GasesActual

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape their escape velocity from the earth, is closest to: [ Boltzmann Constant k B = 1.38 × 10 - 23 J / K Avogadro number N A = 6.02 × 10 26 / k g Radius of Earth: 6.4 × 10 6 m Gravitational acceleration on Earth = 10 m s - 2 ]

Options

  1. A3 × 10 5 K
  2. B650 K
  3. C800 K
  4. D10 4 K

Correct answer

D. 10 4 K

Step-by-step solution

3 RT m = 11 . 2   km / s 3 × 25 3 × T 2 × 10 - 3 = 11 . 2 × 10 3 2 T = 10035 . 2   K ≈ 10 4   K

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