At what temperature will the average velocity of oxygen molecules be sufficient so as to escape from the earth ? Escape velocity of earth is `11.0 kms^(-1)` and mass of one molecule of oxygen is `5.34xx10^(-26)` kg. Boltzmann constant `=1.38xx10^(-23) " J molecule"^(-1) K^(-1)` .

Explanation

For the molecule to just escape from the earth, Average kinetic energy of the molecule at temperature
T = Escape energy of the molecule.
(or) `3/2k_BT=1/2mv_e^2`
`T = (mv_e^2)/(3k_B)`
`=(5.34xx10^(-26)xx(11.0xx10^3)^2)/(3xx1.38xx10^(-23))`
`= 1.56xx10^5 K`.