The ratio of \(v_{\text{rms}} : v_{\text{mp}} : v_{\text{avg}}\) is (symbols have their usual meaning)
\(\sqrt{3} : \sqrt{2} : \sqrt{\frac{\pi}{8}}\)
\(\sqrt{3} : \sqrt{2} : \sqrt{\frac{8}{3}}\)
\(\sqrt{3} : \sqrt{\frac{8}{\pi}} : \sqrt{2}\)
\(\sqrt{3} : \sqrt{2} : \sqrt{\frac{8}{\pi}}\)
Solution:
\[v_{\text{rms}} = \sqrt{\frac{3RT}{M}}\], \[v_{\text{mp}} = \sqrt{\frac{2RT}{M}}\], and \[v_{\text{avg}} = \sqrt{\frac{8RT}{\pi M}}\]. Therefore, \[v_{\text{rms}} : v_{\text{mp}} : v_{\text{avg}} = \sqrt{3} : \sqrt{2} : \sqrt{\frac{8}{\pi}}\].
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