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`.

Options

A. `5.016 xx 10^(4) K`
B. `1.254 xx 10^(4) K`
C. `8.360 xx 10^(4) K`
D. `2.508 xx 10^(4) K`

Answer

C

Explanation

`v_(rms) = sqrt((3 kT)/(m)) = v_(e)`
`(3 kT)/(m) = v_(e)^(2)`
`(3 xx 1.38 xx 10^(-23) T)/(2.76 xx 10^(-26)) = (11.2 xx 10^(3))^(2)`
`T = 8.360 xx 10^(4) K`