For a given gas at a specific absolute temperature , what is the exact mathematical ratio of its roo — States of Matter and Gaseous State Chemistry Question

💡 Solution & Explanation

The formulas are $U_{rms} = \sqrt{3RT/M}$, $U_{avg} = \sqrt{8RT/\pi M}$, and $U_{mp} = \sqrt{2RT/M}$. Taking the ratio $\sqrt{3} : \sqrt{8/\pi} : \sqrt{2} \approx 1.732 : 1.595 : 1.414$. Dividing throughout by $\sqrt{2}$ (1.414) yields exactly $1.224 : 1.128 : 1$.