Question

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is 2 km/s, the root mean square velocity of oxygen at the same condition in km/s is : 

(1) 2.0 

(2) 0.5 

(3) 1.5 

(4) 1.0

Answer 1

Correct option is (2) 0.5 

\(V_{rms} = \sqrt {\frac {3RT}{M}}\)

\(\frac {V_1}{V_2} = \sqrt {\frac {M_2}{M_1}} \Rightarrow \frac{2}{V_2} = \sqrt {\frac {32}{2}}\)

\(V_2 =0.5 \,km/s\)