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While studying about Maxwell-Boltzmann distribution (through a chemistry textbook) I came across the fact that molecules can posses any speed (lower than $c$). This makes it obvious that there are many molecules that have speed greater than escape velocity of the earth. It is then reasonable that some amount of molecules are present at the outer portion of the atmosphere would posses such velocity and hence escape away. This process would continue in a similar fashion so that in a long run a large amount of our atmosphere would have she'd away. Given the fact that earth is 4 billion years old my question is:

  • Why hasn't such thing happened?

  • Why do we still have our significant portion of atmosphere left(if such process had happened)?

Please do correct me wherever I go wrong.

Thanks

1 Answers1

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Mean kinetic energy is related to temperature: $$\langle K_E\rangle=\frac{3}{2}kT=\frac{1}{2}mv^2$$

For example, the average molar mass of air is 29 g/mol, the average $K_E$ of air molecules at 20°C (293K) is approximately $6\times10^{-21}$ J calculated from the equation above. (I assume air is an ideal gas which it isn’t, but it gives an approximate answer)

The average mass of one molecule of air is $4.8\times10^{-26}$ kg and the average speed of one molecule of air at 20°C (293K) is approximately 500 m/s based on my calculation.

The escape velocity on the Earth is 11.2 km/s so you might expect the atmosphere to be constant. However, 500 m/s is the average speed; in fact, some molecules would be travelling faster than this and some would be travelling slower. But the motion itself leads to molecules escaping, and over time all would escape if there were no input of gas into the atmosphere.

Yitian Chen
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