At what temperature is the root mean square velocity of gaseous hydrogen molecules is equal to that of oxygen molecules at `47^(@)C`

Options

A. 20 K
B. 80 K
C. `-73` K
D. 3 K

Answer

A

Explanation

`v_(rms)=sqrt((3RT)/(M)) implies T prop M` [ As `v_(rms)`=constant]
`implies (T_(H_2))/(T_(O_2))=(M_(H_2))/(M_(O_2)) implies (T_(H_2))/((273+47))=(2)/(32) implies T_(H_2) = 20 K`