At what temperature , will the rms speed of oxygen molecules be sufficient for escaping from the earth ? Take `m = 2.76 xx 10^(-26) kg, k = 1.38 xx 10^(-23) J//K and v_(e) = 11.2 km//s`.

Explanation

Translational kinetic energy `= (3)/(2) k T`
The oxygen molecule will escape from earth if
`(3)/(2) k T gt (1)/(2) mv_(e)^(2)`
`T gt (m v_(e)^(2))/(3 k)`
`T gt (((32)/(6.023 xx 10^(23))) xx 10^(-3) xx (11.2 xx 10^(3))^(2))/(3 xx 1.38 xx 10^(-23))`
`T gt 8.36 xx 10^(4) K`