Question
Root mean square velocity of a gas molecule is proportional to
A.
$${m^{\frac{1}{2}}}$$
B.
$${m^0}$$
C.
$${m^{ - \,\frac{1}{2}}}$$
D.
$$m$$
Answer :
$${m^{ - \,\frac{1}{2}}}$$
Solution :
Root mean square speed is given by the expression
$$\eqalign{
& {U_{rms}} = \sqrt {\frac{{3RT}}{M}} \,\,\,\,\left[ {\because \,M = mN} \right] \cr
& \therefore \,\,{U_{rms}} \propto \sqrt {\frac{1}{m}} \cr
& \Rightarrow \,\,{U_{rms}} \propto {\left( m \right)^{ - \frac{1}{2}}} \cr} $$