At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at `47^(@)C`?

Options

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

Answer

D

Explanation

`V_("rms") = sqrt((3RT)/(M))`
Where `T` is the temperature of the gas molecules in kelvin and `M` is the molecules mass of the gas
`V_(H_(2))= V_(O_(2)) implies sqrt((T_(H_(2)))/(M_(H_(2)))) = sqrt((T_(O_(2)))/(M_(O_(2)))) implies (T_(H_(2)))/(2) = (320)/(32) implies T_(H_(2)) = 20K`