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PART - 2 CH - 12 Kinetic Theory — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 12 Kinetic Theory2 Marks
Question
At what temperature will the root mean square velocity of helium molecules be half the root mean square velocity of hydrogen molecules at normal temperature and pressure?
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Answer

Suppoose $C _{ He ( rms )}$ of helium molecules at temperature T will be half of $C _{ H ( rms )}$ of hydrogen at normal temperature and pressure.
So, $\quad C_{He(rms)}=\sqrt{\frac{3 RT}{M_{He}}}$
and $\quad C_{H(rms)}=\sqrt{\frac{3 \times R \times 273}{M_{H}}}$
but $\quad C _{ H ( rms )}=\frac{1}{2} C _{ H ( rms )}$
So, $\quad \sqrt{\frac{3 \times R \times T}{M_{He}}}=\frac{1}{2} \sqrt{\frac{3 \times R \times 273}{M_{H}}}$
On squaring both sides,
or $\quad \frac{T}{M_{He}}=\frac{273}{4 M_{H}}$
or $\quad T=\frac{273 \times M_{He}}{4 M_{H}}=\frac{273 \times 4}{4 \times 2}$
$\quad\quad T=136.5 K$
Hence, that temperature will be 136.5 K .

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