The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at 47° C is (molecular weight of hydrogen and oxygen are 2 and 32 respectively) (a) 47° C (b) 132° C (c) 320° C (d) 405° C

Answer: (b). vrms = √(3RT/M), so (vH)/(vO) = √((TH)/(TO)·(MO)/(MH)) TO = 47 + 273 = 320 K, (MO)/(MH) = 16 4.5² = (16 TH)/(320) ⇒ 20.25 = TH/20 ⇒ TH = 405 K So the answer is (b) 132.

The temperature at which r.m.s. velocity of hydrogen molecules is 4.5… | MHT CET 2026 (17 Apr, Shift 2)

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Molecular Speeds & Maxwell Distribution

The temperature at which r.m.s. velocity of hydrogen molecules is 4.5 times that of an oxygen molecule at $47^\circ$ C is (molecular weight of hydrogen and oxygen are 2 and 32 respectively)

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Answer: (b)

$v_{rms} = \sqrt{\frac{3RT}{M}}$ , so $\frac{v_H}{v_O} = \sqrt{\frac{T_H}{T_O}\cdot\frac{M_O}{M_H}}$
$T_O = 47 + 273 = 320\text{ K}$ , $\frac{M_O}{M_H} = 16$
$4.5^2 = \frac{16\,T_H}{320} \Rightarrow 20.25 = \frac{T_H}{20} \Rightarrow T_H = 405\text{ K}$
So the answer is (b) $132^\circ\text{C}$ .

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