Let vAVG , vRMS  and vMP denote mean speed, rms speed and most probable speed, respectively, of the molecules in an ideal monatomic gas at absolute temperature T. The mass of a molecule is m. Then,

According to the kinetic theory of gases, a molecule of a gas can have any speed between 0 and ¥. Thus, (1) and (2) are obviously wrong.Also, vRMS=3RTM;  vAVG=8RTπM;   vMP=2RTM .  So, vRMS>vAVG>vMP  EAVG=12mvRMS2=12m3kTm=32kT     (1)But  vMP=2kTm⇒kT=12mvMP2.        (2)Using (2) in (1),⇒EAVG=34mvMP2.