(a) Show that the root mean square velocty vrms isBecause + + = , it follows that 1/2 = (I?/M)1/2 = vrms/31/2.The results cart also be obtained directly from the expression in chapter for the average kinetic energy of an ideal gas. (b) Show that the most probable value of the speed vmp isvmp =(2I?/M)1/2.By most probable value of the speed we mean the maximum of the Maxwell distribution as a function of v. Notice that v?^?p <>(c) Show that the mean sped c isThe mean speed may also be written as <|v|>. The ratiovrms/c = 1.086.(d) Show that cz, the mean of the absolute value of the z component of the velocity of an atom, isCz ?! <|vz|> = 1/2 c =(2I?/I?M)1/2.
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