The absolute temperature at which the rms speed of hydrogen molecule is equal to its (where ,R is radiud of moon is r,g acceleration due to gravity on Moon's surface , m is mass of hydrogen molecules and k is Boltzmann constant ).

Options

A. `(mgR)/(2k)`
B. `(2mgR)/(k)`
C. `(3mgR)/(2k)`
D. `(2mgR)/(3K)`

Answer

D

Explanation

`v_(rms)"(hydrogen)"= sqrt((3RT)/(M))=sqrt((3kT)/(m))`
and `v_("escape")"(moon)"=sqrt(2gR)`
`V_(rms)=V_("esacape")`
`rArr (3kT)/(m)=2gR rArr T = (2mgR)/(3k)`