Question

write expression for and define the following 1 maximum provable velocity 2 root mean value of velocity 3 root mean square of velocity

Answer 1

The maximum or most probable speed is the speed at which a particle picked at random from a gaseous sample is most likely to be travelling. It corresponds to the speed at which the Maxwell-Boltzmann distribution of speeds is at a maximum. Only a small fraction of particles might have this speed, but it is more likely than any other speed.
${\mathrm{v}}_{\mathrm{mp}}=\sqrt{\frac{2\mathrm{RT}}{\mathrm{M}}}$
Root mean square velocity is the average velocity of the molecules of a gas.
${\mathrm{v}}_{\mathrm{rms}}=\sqrt{\frac{3\mathrm{RT}}{\mathrm{M}}}$

where, R = Gas constant

M = Molar mass of the gas

T = temperature of the gas.