At what temperature is `v_(rms)` of `H_(2)` molecules equal to the escape speed from earth's surface. What is the corresponding temperature for escape of hydrogen from moon's surface ? Given `g_m = 1.6 m//s^(2), R_e = 6367 km "and" R_m = 1750 km`.

Answer

A, D

Explanation

(i) `sqrt((3 R T)/(M)) = 11.2 xx 10^3 m//s`
`:. T = ((11.2 xx 10^3)^2 M)/(3 R)`…(i)
=`((11.2 xx 10^3)^2 xx 2 xx 10^-3)/(3 xx 8.31)`
=`10059 K`
(ii) Escape velocity from moon
= `(sqrt (2 g _m R_m))`
= `(sqrt(1.6 xx 2 xx 1750 xx 10^3))`
=`2366 m//s`
Substituting in Eq. (i), we have
`T = ((2366)^2 xx 2 xx 10^-3)/(3 xx 8.31)`
= `449 K`.