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JEE Main202621 January 2026Evening ShiftPhysicsKinetic Theory of GasesActual

The r.m.s. speed of oxygen molecules at 47^ C is equal to that of the hydrogen molecules kept at _ _ _ _ ^ C . (Mass of oxygen molecule/mass of hydrogen molecule =32 / 2 )

Options

  1. A-235
  2. B-253
  3. C-100
  4. D-20

Correct answer

B. -253

Step-by-step solution

The root-mean-square speed of gas molecules is: v_ rms = 3RT M , where T is absolute temperature and M is molar mass. For oxygen at T₁ = 47°C = 320 K with M_ O₂ = 32 g/mol: v_ rms,O₂ = 3R(320) 32 For hydrogen with M_ H₂ = 2 g/mol at temperature T₂ : v_ rms,H₂ = 3RT₂ 2 Equating the RMS speeds: 3R(320) 32 = 3RT₂ 2 320 32 = T₂ 2 T₂ = 2 10 = 20 K Converting to Celsius: t₂ = 20 - 273 = -253°C , which is option (2).

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