At what temperature will the rms speed of oxygen molecules become just sufficient for escaping from the Earth's atmosphere ? (Given : Mass of oxygen molecule (m) `= 2.76 xx 10^(-26) kg` , Boltzmann's constant `k_B = 1.38 xx 10^(-23) JK^(-1)` )

Options

A. `2.508xx10^4K`
B. `8.360xx10^4K`
C. `5.016xx10^4K`
D. `1.254xx10^4K`

Answer

B

Explanation

Escape speed `(V_(es)) = V_(rms)`
`rArr 11.2 xx 10^3 = sqrt((3kT)/(m))`
`rArr T = ((11.2xx 10^3)^2 xx 2.76 xx 10^(-26))/(3 xx 1.38 xx 10^(-23))`
`rArr T = 8.360 xx 10^4 K`