At a height of 200 km above the earth's surface, in the thermosphere, the atmosphere is almost entirely nitrogen (N2) The pressure is approximately 70 nPa (7 X 10-8 Pa) and the temperature approximately 900 K. The earth's escape velocity is 11.2 km s-1.
a. What fraction of the nitrogen molecules in the thermosphere have velocities greater than the earth's escape velocity?
b. Molecules which have velocities in excess of the earth's escape velocity in the radial (outward) direction can escape the earth's gravity into space (if they do not collide). What fraction of molecules have radial components of velocity in excess of the earth's escape velocity?
c. How many nitrogen molecules will there be in a 1 km thick shell of the thermosphere, if the inner distance of the shell from the earth's surface is 200 km? (The earth's radius is 6353 km.) How many of these molecules will have enough radial velocity to escape?
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