`
`
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 $0^{\circ} \mathrm{C}$.
Correct Option: 1
Solution:
$\mathrm{V}_{\mathrm{rms}}=\sqrt{\frac{3 \mathrm{KT}}{\mathrm{M}}}$
$\left(\mathrm{V}_{\mathrm{rms}}\right)_{\mathrm{O}_{2}}=\sqrt{\frac{\mathrm{M}_{\mathrm{H}_{2}}}{\mathrm{M}_{\mathrm{O}_{2}}}}=\sqrt{\frac{2}{32}}$
$\left.\left(\mathrm{~V}_{\mathrm{rms}}\right)_{\mathrm{H}_{2}}\right)_{\mathrm{H}_{2}}=4 \times\left(\mathrm{V}_{\mathrm{mus}^{\mathrm{ms}}}\right)_{\mathrm{O}_{2}}$
$=4 \times 160$
$=640 \mathrm{~m} / \mathrm{s}$
.jpg)