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:
Using standard molecular velocity expressions: \(v_{\text{rms}} = \sqrt{\frac{3RT}{M}}\), \(v_{\text{mp}} = \sqrt{\frac{2RT}{M}}\), and \(v_{\text{avg}} = \sqrt{\frac{8RT}{\pi M}}\). This gives the ratio \(\sqrt{3} : \sqrt{2} : \sqrt{\frac{8}{\pi}}\).
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