At what temperature the mean speed of the molecules of hydrogen gas equals the escape speed from the earth?

Explanation

Mean speed `bar(v) = sqrt((8 R T)/(pi M_(0)))`
Escape velocity `v_(e) = sqrt(2 g R_(e)) = 11.2 km//s`
`=11.2xx10^(3) m//s`
`bar(v) = v_(c )`
`sqrt((8 R T)/(pi M_(0))) = 11.2 xx 10^(3)`
`(8 R T)/(pi M_(0)) = (11.2 xx 10^(3))^(2)`
`(8 xx 8.3 xxT)/(pi xx 2 xx 10^(-3)) = (11.2)^(2) xx 10^(6)`
`T = 11864 K`