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

Options

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

Answer

B

Explanation

`v_("rms")=sqrt((3RT)/(M))`
`therefore(v_("rms"))_(O_(2))=(v_("rms"))_(H_(2))`
`thereforesqrt((RT_(O_(2)))/M_(O_(2)))=sqrt((RT_(H_(2)))/(M_(H_(2))))" "thereforeM_(O_(2))=32andM_(H_(2))=2`
`thereforesqrt((273+47)/32)=sqrt(T/2)" "thereforesqrt(320/32)=sqrt(T/2)`
`thereforeT/2=10" "thereforeT=20K`