Kinetic Theory of Gases & Escape Speed

[emperrotta]

Homework Statement

In the first 2 parts of the problem, I calculated at what temperatures the rms speeds v_rms of H₂ molecules and O₂ molecules would equal the escape speed of Earth (11200 m/s). The answers I calculated for this were 10000 K for H₂ and 160000 K for O₂. Those answers are correct according to the back of the textbook.

The last part of the question states: Considering the answers to parts (a) and (b), should there be much hydrogen and oxygen high in the Earth's upper atmosphere, where the temperature is about 1000 K?Attempt at a solution
According to the back of the textbook, the answer is no for H₂ and yes for O₂.

My thought process was the answer is yes for both because the temperature of 1000 K high in the Earth's upper atmosphere is small relative to both the temperatures I calculated (10000 K for hydrogen and 160000 K for oxygen). Thus the temperatures of either gas molecules will not reach a high enough temperature to have a large fraction of the molecules of either gas reach the escape speed of Earth.

How is the answer no for hydrogen? What am I missing here?

 

[Gear300]

I'm not sure how high up in the atmosphere 1000 K would correspond to, but the escape speed taken in respect to that elevation should be less than when taken at the surface of Earth.

Just a side question...the atmosphere would be 1000 K for when it is facing the sun, right (that seems a bit high otherwise)?