Question

The composition of planetary atmospheres is determined in part by the speeds of the molecules of the constituent gases because the faster moving molecules can reach escape velocity and leave the planet (often called Jeans escape, named after British astronomer Sir James Jeans). The major constituents of earth’s atmosphere (air) are nitrogen, oxygen, argon, carbon dioxide, dihydrogen monoxide, neon, helium, methane, krypton and hydrogen gases. In general, the earth is too large to lose a significant proportion of its atmosphere through Jeans escape. (A) Of the major constituent gases in the earth’s atmosphere, which are most susceptible to Jeans escape? (B) The exosphere is the high-altitude region where atmospheric density is sparse and Jeans escape occurs. For the atmospheric gases susceptible to Jeans escape (part-A), estimate the fraction of molecules traveling at a speed above the earth’s escape velocity.

Answer 1

A)

Finding the most susceptible to jeans escape

Hydrogen and other lighter gases are most susceptible to jeans out of all major constituents of the earth’s atmosphere

This leads to escape because they easily overcomes the gravity of earth

B)

Since the rate of escape is very low, the molecules that will escape from the atmosphere are moving at a speed above earth’s escape velocity.

We know for Hydrogen it is 3 kg/s

And for Helium it is 0.05 kg/s

From the above data which are moving at a speed lighter then escape velocity are a very small fraction of molecules

When the gravitational potential energy becomes lesser then the thermal energy there is a possibility of escape occurs

KT=1/2 m v 2>Gm M/R