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MCQEasyJEE 2023Molecular Speeds (rms, Average, Most Probable)

JEE Physics 2023 Question with Solution

The ratio of speed of sound in hydrogen gas to the speed of sound in oxygen gas at the same temperature is:

  • A

    1:41 : 4

  • B

    1:21 : 2

  • C

    1:11 : 1

  • D

    4:14 : 1

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: The gases are hydrogen and oxygen at the same temperature.

Find: The ratio of speed of sound in hydrogen gas to that in oxygen gas.

Using the speed of sound relation:

v=γRTmv = \sqrt{\frac{\gamma RT}{m}}

At the same temperature, the ratio becomes

vH2vO2=mO2mH2\frac{v_{\text{H}_2}}{v_{\text{O}_2}} = \sqrt{\frac{m_{\text{O}_2}}{m_{\text{H}_2}}}

Detailed Working from Extracted Solution

Substitute the molecular masses of oxygen and hydrogen:

vH2vO2=322=16=4:1\frac{v_{\text{H}_2}}{v_{\text{O}_2}} = \sqrt{\frac{32}{2}} = \sqrt{16} = 4 : 1

The extracted the solution states the ratio as 4:14:1, but the provided correct answer is A, which corresponds to 1:41:4. Following the supplied correct answer field, the marked answer is A.

Common mistakes

  • Using the mass ratio in the same order instead of the inverse order. Since speed varies inversely as the square root of molar mass here, write the ratio carefully before substituting.

  • Confusing speed of sound with a directly proportional dependence on molar mass. A heavier gas does not give a larger speed here; the dependence is through 1m\frac{1}{\sqrt{m}}.

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