Question

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`.

Answer 1

If the temperature is T, according to kinetic theory of gases translational `KE=(3)/(2)K_(B)T`
The oxygem molecule will escape from earth
if `(3)/(2)kTgt(!)/(2)mv_(e)^(2)` i.e. `Tgt(mv_(e)^(2))/(3k)` (or)
`Tgt(2.76xx10^(-26)xx(11.2xx10^(3))^(2))/(3xx1.38xx10^(-23))Tgt8.36xx10^(4)K`