Kinetic Theory

JEE Main level, single correct, medium

64 of 168

Question 64 of 168

At room temperature a diatomic gas is found to have an r.m.s. speed of 1930 ms−11930 \mathrm{~ms}^{-1}. The gas is:

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Answer: (A) H2\mathrm{H}_2

∵C=3RTM(19302)=3×8.314×300MM=3×8.314×3001930×1930≈2×10−3 kg\begin{aligned} &\because \quad \mathrm{C}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}} \\ &\left(1930^2\right)=\frac{3 \times 8.314 \times 300}{\mathrm{M}} \\ &\mathrm{M}=\frac{3 \times 8.314 \times 300}{1930 \times 1930} \approx 2 \times 10^{-3} \mathrm{~kg} \end{aligned}
The gas is
H2\mathrm{H}_2.

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