Equating two formulas for root-mean-square velocity

[JC2000]

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)

 

[kuruman]

If by "molecular mass" you mean the mass of one molecule, then all of the above is correct.

 

[JC2000]

If by "molecular mass" you mean the mass of one molecule, then all of the above is correct.

Yes, thanks for going through it all!