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JEE Main202430 Jan 2024Morning ShiftPhysicsKinetic Theory of GasesActual

At which temperature the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at 47 ° C ?

Options

  1. A80 K
  2. B- 73 K
  3. C4 K
  4. D20 K

Correct answer

D. 20 K

Step-by-step solution

The r.m.s velocity of the molecule of a gas of molecular weight M at Kelvin temperature T is given by, V r m s = 3 R T M . Let M O and M H are molecular weight of oxygen and hydrogen and T O and T H the corresponding Kelvin temperature at which V r . m . s is same for both, V r . m . s = 3 R T O M O = 3 R T H M H . Hence T O M O = T H M H T O = 273 ° C + 47 ° C = 320 K , M O = 32 , M H = 2 ⇒ T H = 2 32 × 320 = 20 K

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