Here, we have to find out the relation between root mean square velocity of gas molecules and temperature We have the expression for rms velocity as Vrms = √
3RT
M
where M - molar mass T - temperature R - Universal gas constant But, M = Nm where N is Avogadro number and m is mass of a molecule ∴ Vrms = √
3RT
Nm
= √
3kT
m
Boltzman constant k =
R
N
∴ Vrms α √
1
m
at a given temperature or Vrms α m
1
2
that is, root mean square velocity of gas molecules at a given temperature is inversely proportional to the square root of the mass of gas molecules