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JEE Main2014PhysicsKinetic Theory of GasesActual

Modern vacuum pumps can evacuate a vessel down to a pressure of 4.0 × 1 0 - 1 5 atm. at room temperature (300 K). Taking R = 8.3 JK -1 mole -1 , 1 atm = 10 5 Pa and N Avogadro = 6 × 1 0 2 3 mole - 1 , the mean distance between molecules of gas in an evacuated vessel will be of the order of :

Options

  1. A0 . 2  μm
  2. B0 . 2   mm
  3. C0 . 2   cm
  4. D0 . 2   nm

Correct answer

B. 0 . 2   mm

Step-by-step solution

Let the inter molecular distance be D Then in a volume of 4 3 π D 3 there is only one molecule. 4 3 π D 3 P = ( 1 N A ) R T D = ( 3 R T 4 π N A P ) 1 3 Substituting P = 4 × 10 − 10 P a , R = 8.3 , N A = 6 × 10 23 , T = 300 K D = 0.2 m m

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