"I suppose the surprising thing is why the atmosphere doesn’t all fall immediately to the Earth’s surface to form a thin dense layer of air molecules.
The reason this doesn’t happen is that air molecules are all whizzing around at surprisingly high speeds - typically hundreds of metres per second depending on the temperature.
The air molecules bash into each other and knock each other around, and the air molecules near the ground bash into the air molecules above them and stop them falling down."
If it were zero then all the air would indeed just fall down to the ground (actually, this is a simplification I’ll address later).
As you increase the temperature the atoms of the ground will start to wiggle more and they’ll start to kick the air molecules giving them non-zero average height.
So the atmosphere would move a little off the ground. The bigger the temperature is the higher the atmosphere will reach.
Note: there are number of assumptions above that simplify the picture. They are not that important but I want to provide a complete picture:
1, Even at the zero temperature the molecules would wiggle a little because of quantum mechanics
2, The atmosphere would freeze at some point (like 50K) so under that temperature it would just lie on the ground
3, I assumed that the ground and the atmosphere have the same temperature because they are in the thermal equilibrium; in reality their temperatures can differ a little because of additional slow heat-transfer processes."
This is the way! It helps me to imagine what would it look like if the atmosphere consisted of a single nitrogen molecule. You place it on the ground but the ground has temperature (is warm) so your one molecule gets launched up into the vacuum on a parabolic trajectory at 500 m/son average. If it launched at 45° it would reach 6km up and fall down, at 90° - 12km up - and that’s on average. Some would get launched faster and higher (following the long tail of the Boltzmann distribution), and hydrogen and helium even faster still because they are lighter. A few hydrogen molecules would be launched at speed above 11km/s, which is above Earth’s escape velocity, so they would escape and never fall down.
When you have many air molecules, they hit each other on the way up (and down), but because their collisions must be perfectly elastic, mathematically it works out that the overall velocities are preserved. So when your one nitrogen molecule gets launched up but on its way hits another identical molecule, you can think of them equivalently as passing through each other without colliding at all. (Yes, mathematically they can also scatter in some other random directions, but the important part is that your original molecule is equally likely to be boosted further upwards as opposed to impeded.)
The end result is that majority of the atmosphere stays below 12km, density goes down as you go up though never quite reaching zero, and hydrogen and helium continuously escape to space to the point none are left.
According to this physics.stackexchange.com answer:
"I suppose the surprising thing is why the atmosphere doesn’t all fall immediately to the Earth’s surface to form a thin dense layer of air molecules.
The reason this doesn’t happen is that air molecules are all whizzing around at surprisingly high speeds - typically hundreds of metres per second depending on the temperature.
The air molecules bash into each other and knock each other around, and the air molecules near the ground bash into the air molecules above them and stop them falling down."
Detailed explanation from another answer:
"The key ingredient is temperature.
If it were zero then all the air would indeed just fall down to the ground (actually, this is a simplification I’ll address later).
As you increase the temperature the atoms of the ground will start to wiggle more and they’ll start to kick the air molecules giving them non-zero average height.
So the atmosphere would move a little off the ground. The bigger the temperature is the higher the atmosphere will reach.
Note: there are number of assumptions above that simplify the picture. They are not that important but I want to provide a complete picture:
1, Even at the zero temperature the molecules would wiggle a little because of quantum mechanics
2, The atmosphere would freeze at some point (like 50K) so under that temperature it would just lie on the ground
3, I assumed that the ground and the atmosphere have the same temperature because they are in the thermal equilibrium; in reality their temperatures can differ a little because of additional slow heat-transfer processes."
This is the way! It helps me to imagine what would it look like if the atmosphere consisted of a single nitrogen molecule. You place it on the ground but the ground has temperature (is warm) so your one molecule gets launched up into the vacuum on a parabolic trajectory at 500 m/s on average. If it launched at 45° it would reach 6km up and fall down, at 90° - 12km up - and that’s on average. Some would get launched faster and higher (following the long tail of the Boltzmann distribution), and hydrogen and helium even faster still because they are lighter. A few hydrogen molecules would be launched at speed above 11km/s, which is above Earth’s escape velocity, so they would escape and never fall down.
When you have many air molecules, they hit each other on the way up (and down), but because their collisions must be perfectly elastic, mathematically it works out that the overall velocities are preserved. So when your one nitrogen molecule gets launched up but on its way hits another identical molecule, you can think of them equivalently as passing through each other without colliding at all. (Yes, mathematically they can also scatter in some other random directions, but the important part is that your original molecule is equally likely to be boosted further upwards as opposed to impeded.)
The end result is that majority of the atmosphere stays below 12km, density goes down as you go up though never quite reaching zero, and hydrogen and helium continuously escape to space to the point none are left.