Question

If average velocity of a sample gas molecules at $300K$ is $5cm{s}^{-1}$, what is RMS veolocity of sample of gas molecules at the same temperature?(Given, $U_{rms}:U_{av}=1.224:1.127$)

• A. $6.112cm/s$
• B. $2.605cm/s$
• C. $4.605cm/s$
• D. $5.430cm/s$

Answer 1

The correct option is D $5.430cm/s$

Root mean square velocity is

$\Rightarrow U_{rms}=\sqrt{\frac{3RT}{M}}$

Average velocity is

$U_{avg}=\sqrt{\frac{8RT}{\pi M}}$

at $T=300K$ $U_{avg}=3.5cm{s}^{-1}$

$\Rightarrow 5cm{s}^{-1}\sqrt{\frac{8R\times 300}{\pi M}}=\sqrt{\frac{8\times 3\times R\times 7}{3\times \pi \times M}}$

$\Rightarrow 5cm{s}^{-1}=\sqrt{\frac{8}{3\pi }}\times \sqrt{\frac{3RT}{M}}=\sqrt{\frac{8}{3\pi }}{M}_{rms}$

$\Rightarrow M_{rms}=5.427cm{s}^{-1}=5.43sm{s}^{-1}$