the root mean squared velocity would not change if the particle was an air or in hydrogen gas.
The root mean square velocity is the square root of the average of the square of the velocity. As such, it's units of velocity. the rationale we use the rms velocity instead of the average is that for a typical gas sample the net velocity is zero since the particles are moving in all directions.
RMS stands for the basis mean square speed.
This is the square root of the average (mean) of all of the square of the speeds of individual particles in a gas.
Calculation of RMS :
The root mean square (R.M.S) speed V of the molecules of a perfect gas is given by the expression, v=sqrt(3RTM) and v=sqrt(3KTm) where R is universal universal gas constant , T is that the absolute (Kelvin) temperature, m is that the molar mass, K is Boltzmann's constant and M is the molecular mass.
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