Correct Answer - Option 1 :
\(\sqrt{\dfrac{M_2}{M_1}}\)
CONCEPT
-
Root Mean Square Speed is defined as the square root of the mean of squares of the speed of different molecules.
- The root-mean-square speed takes into account both molecular weight and temperature, two factors that directly affect the kinetic energy of a material.
- The RMS speed of any homogeneous gas sample is given by:
\(V_{rms}= \sqrt {\frac{{3RT}}{M}} \)
Where R = universal gas constant, T = temperature and M = molar mass
CALCULATION:
Let V1 be the RMS speed of gas of molecular weight M1;
V2 be the RMS speed of gas of molecular weight M2;
Now at a temperature, the ratio of speeds will be
\(\frac {V_1}{V_2} = \frac {\sqrt {\frac {3RT}{M_1}}}{\sqrt {\frac {3RT}{M_2}}}\)
\(\Rightarrow \frac {V_1}{V_2} = \sqrt {\frac {M_2}{M_1}}\)