d
\({v_{rms}} = \sqrt {\frac{{3RT}}{M}} ,\) \({v_P} = \sqrt {\frac{{2RT}}{M}}  = 0.816{v_{rms}}\)

\(\bar v = \sqrt {\frac{{8RT}}{{\pi M}}}  = 0.92{v_{rms}}\) \( \Rightarrow \,\,{v_P} < \bar v < {v_{rms}}\)

and \({E_{av}} = \frac{1}{2}mv_{rms}^2 = \frac{1}{2}m\frac{3}{2}v_P^2 = \frac{3}{4}mv_P^2\)