If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen molecule at 47, the temperature of hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are 2 and 32 respectively) (a) 23 (b) 47 (c) 80 (d) 114

Answer: (b). (vH)/(vO) = √((TH)/(TO)·(MO)/(MH)) with TO = 320 K, (MO)/(MH) = 16 16 = (16 TH)/(320) ⇒ TH = 320 K So the answer is (b) 47.

If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen… | MHT CET 2025 (19 Apr, Shift 2)

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Molecular Speeds & Maxwell Distribution

If r.m.s. velocity of hydrogen molecules is 4 times that of an oxygen molecule at $47^\circ\text{C}$ , the temperature of hydrogen molecules is (Molecular weight of Hydrogen and Oxygen are 2 and 32 respectively)

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Answer: (b)

$\frac{v_H}{v_O} = \sqrt{\frac{T_H}{T_O}\cdot\frac{M_O}{M_H}}$ with $T_O = 320\text{ K}$ , $\frac{M_O}{M_H} = 16$
$16 = \frac{16\,T_H}{320} \Rightarrow T_H = 320\text{ K}$
So the answer is (b) $47^\circ\text{C}$ .

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