# Equating two formulas for root-mean-square velocity

## Homework Statement:

Compare ##v_{rms}##, ##v_{most probable}## and ##v_{average}## (arrange them in increasing/decreasing order).

## Relevant Equations:

##v_{rms} = \sqrt {\frac{3RT}{M}}## where ##M## is molar mass of the gas. ... (1)
##v_{rms} = \sqrt {\frac{3k_{B}T}{m}}## where ##m## is the molecular mass of the gas. ...(2)
## N_A*k_B = n*R## where ##N_A## is Avogadro's number and ##n## is the number of moles of the gas.
## \frac{M}{N_A} = m## (?)
(a)
My question :
Are all the formulas correct?

If so I can write ##v_{rms}## in form (2) and compare that result with the other velocities to get the answer (rms > average > most probable)

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