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kinetic theory-would you please explain rms-speed? how can we derive the equation for the same?

Root mean square speed : It is defined as the square root of the mean of the square of the speeds of the individual molecules of a gas. If v₁, v₂, v₃, ...., v_n are the speeds of the n gas molecules, then the root mean square speed for the gas is given by

From Maxwell's speed distribution law, it can be seen that

Thus, the root mean square speed of the gas molecules is directly proportional to the square root of the temperature of the gas.

At a given temperature,

Hence for lighter gases, the r.m.s. speed is comparatively high, as it depends inversely upon the square root of its molecular mass. The r.m.s. speed of hydrogen molecules is four times that of oxygen molecules at the same temperature.