# Why do individual helium atoms rise?

Balloons full of helium rise because the buoyant force is great than the gravitational force and the buoyant force is due to a pressure difference between the top and bottom of a ballon but why exactly does a individual helium atom rise?

• Basically the same reason, albeit more at a granular/stochastic level. Mix a small piece of styrofoam in some sand and start shaking it to mimick air molecules flying around. The styrofoam will end up on top. Or conversely you could put some gold chunks in some sand and pan it out the other way Sep 9 at 0:07
• @R.Rankin I think the examples you give of the Brazil nut effect are more about the difference in size of the particles, rather than the density. Helium gas in a gaseous mixture is different.
– Noah
Sep 11 at 0:00

The probability that an energy level, $$E$$, is occupied is given by the Boltzmann factor:

$$P\propto e^{-\frac E {kT}} = e^{-\frac{mgh}{kT}}$$

where $$m$$ is the species mass. The scale height is then:

$$\bar h = \frac{kT}{mg}$$

For $${\rm N}_2$$ you around 8,000 meters, while helium is 7x higher. Oxygen ($$m\approx\,$$32) is even lower at 7200 meters, so in the death zone (above 8000m) alpinist have less the $$1/e$$ the oxygen available at sea level.

• Why is single emphasized? A single helium atom is going to be at a random height. It moves randomly with a higher average height than other heavier molecules. Have you ever seen a Markov process away from its mean?
– JEB
Sep 9 at 2:59
• @josephh buoyancy is a statistical effect due to the interactions of an ensemble of atoms . If one has just a helium atom in vacuum and gravity, it would fall. So the OP is asking about the effective forces on an individual atom in the ensemble, i.e. at the quantum level. Sep 9 at 4:24
• @JEB could you give a link for the expressions? Sep 9 at 4:25
• @JEB Yes, that is where I misunderstood what the OP was asking. Thanks Sep 9 at 4:32
• – JEB
Sep 9 at 16:29