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If the rms speed of oxygen

Question:

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

  1. $640 \mathrm{~m} / \mathrm{s}$

  2. $40 \mathrm{~m} / \mathrm{s}$

  3. $80 \mathrm{~m} / \mathrm{s}$

  4. $332 \mathrm{~m} / \mathrm{s}$


Correct Option: 1

Solution:

$\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{KT}}{\mathrm{M}}}$

$\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}=\sqrt{\frac{\mathrm{M}_{\mathrm{H}_{2}}}{\mathrm{M}_{\mathrm{O}_{2}}}}=\sqrt{\frac{2}{32}}$

$\left.\left(\mathrm{~V}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}\right)_{\mathrm{H}_{2}}=4 \times\left(\mathrm{V}_{\mathrm{mus}^{\mathrm{ms}}}\right)_{\mathrm{O}_{2}}$

$=4 \times 160$

$=640 \mathrm{~m} / \mathrm{s}$

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