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The ratio of root mean square velocity of hydrogen at $50 \mathrm{~K}$ to that of nitrogen at $500 \mathrm{~K}$ is closest to
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$1.18$
$\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{RT}}{\mathrm{M}}}$
$\frac{\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}}{\left(\mathrm{~V}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}}=\frac{\sqrt{\frac{3 \times \mathrm{R} \times 50}{2}}}{\sqrt{\frac{3 \times \mathrm{R} \times 500}{28}}}=1.18$
$\frac{\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}}{\left(\mathrm{~V}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}}=\frac{\sqrt{\frac{3 \times \mathrm{R} \times 50}{2}}}{\sqrt{\frac{3 \times \mathrm{R} \times 500}{28}}}=1.18$
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