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  4. The root mean square velocity of hydrogen molecules at 300 K is 1930 m s-1. The rms velocity of oxygen molecules at 1200 K will be

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Q. The root mean square velocity of hydrogen molecules at $300 \,K$ is $1930\, m \,s^{-1}$. The rms velocity of oxygen molecules at $1200\, K$ will be

Kinetic Theory

Solution:

$\upsilon_{rms} = \propto\sqrt{T / M}$
$\therefore \quad\left(\upsilon_{O}\right)_{rms} = \sqrt{\frac{T_{O} / M_{O}}{T_{H} / M_{H}}} = \sqrt{\frac{T_{O}}{T_{H}}\times\frac{M_{H}}{M_{O}}}$
$\left(\upsilon _{H}\right)_{rms} = \sqrt{\frac{1200}{300}\times\frac{2}{32}} = \frac{1}{2}$
$\therefore \quad \left(\upsilon _{O}\right)_{rms} =\frac{1}{2} \upsilon _{H} = \frac{1}{2}\times1930 = 965\,m\,s^{-1}$