If the rms speed of oxygen molecules at 0^{} {C} is 160 {m/s}, find the rms speed of hydrogen molecules at 0^{} {C}.

Correct Answer is : 640m/s640 {m/s}640m/s

Correct Answer is : 640m/s640 {m/s}640m/s

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BITSAT 2025 Shift 2 Paper

Question : 4 of 130

Marks: +1, -0

0^{\circ} \mathrm{C}

160 \text{m/s}

0^{\circ} \mathrm{C}

Solution:

Root mean square speed is given by

v_{r m s} = \sqrt{\; \frac{3 k T}{M}} \Rightarrow v_{r m s} \propto \; \frac{1}{M}

\therefore \; \frac{(v_{r m s})_{O_{2}}}{(v_{r m s})_{H_{2}}} = \sqrt{\; \frac{M_{H_{2}}}{M_{O_{2}}}}

\Rightarrow \; \frac{(v_{r m s})_{O_{2}}}{(v_{r m s})_{H_{2}}} = \sqrt{\; \frac{2}{32}} = \; \frac{1}{4}

\Rightarrow (v_{r m s})_{H_{2}} = 4 \times (v_{r m s})_{O_{2}}

( \because (v_{r m s})_{O_{2}} = 160 \text{m/s} )

= 4 \times 160 = 640 \text{m/s}

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