12. The Maxwell speed distribution P(v) is a function such that P(v)dv gives the fraction of molecules with speeds in the interval dv at speed v. One has

$P(v) = 4\pi \left(\frac{M}{2\pi RT}\right)^{3/2} v^2 e^{-Mv^2 / 2RT}$. The root-mean-square speed of the molecule is defined as $v_{rms}^2 \equiv \int v^2 P(v) dv$, while the average speed of the molecule is defined as $v_{avg} \equiv \int v P(v) dv$. Furthermore the most probable speed $v_p$ is the speed at which $P(v)$ is maximum. We have

(A)$v_{p} > v_{rms} > v_{avg}$
(B)$v_{p} > v_{avg} > v_{rms}$
(C)$v_{rms} > v_{p} > v_{avg}$
(D)$v_{avg} > v_{rms} > v_{p}$

(E)None of the above