Why does helium rise?

Now, I understand, or at least I’m familiar with Archimedes’ Principle and buoyancy. In other words, I am aware that submerged objects experience an upward force which is equal to their weight minus the weight of the volume of the medium (or fluid) they displace. And, I suppose I could rephrase Archimedes’ Principle to something along the lines of the following: since the pressure is higher at the bottom of a submerged object than at its top (i.e. since, by definition, there is more fluid overlying the bottom than the top), there is a pressure gradient tending to thrust the object upwards.

But, regardless of how Archimedes’ Principle is formulated, I still don’t understand why it works the way it does.

Here’s a question that encapsulates my ignorance of the matter: Does a *single *helium atom rise through the atmosphere, or must there be an enclosed ensemble of helium atoms (i.e. a cell) for them to rise?

If the atoms are contained in, say, a balloon, I understand why they (and the balloon) will rise - the weight of the helium atoms in the balloon is less than the weight of the volume of air that is displaced by the balloon. That’s just Archimedes’ Principle.

On the other hand, if the helium atoms are not confined by the ‘walls’ of a balloon, they would each be ‘individual actors’; there is no cell of helium atoms, no column of air that they are displacing. In fact, when speaking of individual helium atoms, the only thing that I can think of that resembles a volume or a column, is the volume of air displaced by a single helium atom. But, if that’s correct, where does the upward thrust come from? What is pushing the (single) helium atom upwards? Could it possibly be the case that the ‘volume’ occupied by a single helium atom is greater than that occupied by the air molecules (whether nitrogen, oxygen, etc.) by which it is surrounded? So, again, my bottom line question: does a *single *helium atom rise through the air?

Thanks! (And, apologies for the long-winded way that I’ve phrased my question - in part that was to show the background I’m working with and so, perhaps, to give a clue to the more knowledgeable among us where my muddled thinking is coming from and, thus, where to set me straight.)

ETA: I neglected to mention that, empirically, single helium atoms do rise - all the way out of the atmosphere. Hence, my question is rooted in reality.

“single helium atoms do rise - all the way out of the atmosphere” :confused:

Not trying to ‘nitpick’, (especially, since you haven’t received any answers yet) but that phrase ‘all the way out of the atmosphere’ implies (to me) that said helium atoms actually leave the atmosphere. I think that this is not the case, and that it is not what you are inferring.
Am I correct in my understanding, of what you are saying as opposed to what I think you mean? :confused:

Sorry if that’s confusing, but I hope you get what I’m trying to say.

Yes. Its also one of the reasons that helium is actually mined along with natural gas. Because of it being so light, it floats into the sky and is basically lost to us from that point on which is supposed to lead to a massive helium shortage.

From http://en.wikipedia.org/wiki/Helium:

Basically, at the fundamental level, if my understanding is correct, is that it’s basically gravity. Helium atoms, on average, have a tiny bit less force on them than other molecules. They’re all zipping around at hundreds of mph and such, but there’s less of a downward force on an individual He atom than other stuff in the atmosphere, and so, over time, He rises while other stuff on average stays down.

This isn’t quite a WAG but I don’t have a cite either. I won’t be surprised if I’ve way oversimplified it, or am entirely wrong.

being noble it doesn’t care much to mix with common atoms. left to its own devices it is a leaker.

I think it’s related to what you’re discussing, but there’s an important subtlety - it depends on the average velocity of the molecules involved, and, at a given temperature, lighter molecules are travelling faster, on average, and are also more likely to reach speeds that are close to the escape velocity of Earth. Helium atoms, being much lighter than oxygen or nitrogen (the main constituents of the atmosphere) are therefore much more likely to escape than the heaver gases.

http://en.wikipedia.org/wiki/Atmospheric_escape

I do not think that free helium atoms in the air have any more tendency to rise than any other type of gas molecule. They just disperse freely in all directions, and Archimedes’ principle does not apply at this scale. However, those that get high enough (as many inevitably will, via the usual random process of dispersion) will leave the atmosphere altogether and go off into space at a higher rate than will the molecules of heavier gasses such a nitrogen and oxygen [ETA: For the reason given by Dervorin]. This keeps the helium concentration in teh atmosphere as a whole at a low equilibrium. The lighter monoatomic molecules of helium also disperse more quickly than the molecules of heavier gasses. This is because when a helium molecule and a heavier molecule collide, the helium will be accelerated more (by Newton’s second and third laws). Thus, helium released at ground level will disperse more quickly, and some of it will reach the top of the atmosphere more quickly than, say, CO2 released at ground level.

Thanks for thinking about this.

Just to be clear, though, I am using helium mostly as an example. My question is really regarding ‘the why’ - why does any individual “lighter” atom/molecule tend to rise? It can’t be the gravitational difference, can it? The absolute magnitude of such gradients when considered on the atomic/molecular level must be irrelevant, no?

The way I learned to think about it is that at the level of molecules - consider a Helium atom a molecule for this purpose - there is constant roiling and agitation. Heat makes molecules bump against one another constantly even in calm air. But the atmosphere is never truly calm. Air always moves. The number of collisions a molecule undergoes is billions per second.

Any individual molecule of helium may be pushed in any direction. But statistical laws apply to large groups of them. Helium is the lightest molecule, equal to a hydrogen molecule and less than oxygen or nitrogen or carbon dioxide. Gravity does make a difference because (anthropomorphically) it always tugs on the heavier one a bit more, so there is a tendency that in a collision the helium atom will be forced up. You might not see it in a given collision for a given molecule, but over time the effect of trillions of collisions is to force helium atoms ever upward. They will leak slowly into outer space, even though an individual one could be brought back down by random collisions. This would happen to hydrogen too, except that it has a tendency to combine with oxygen, fall as water, and be kept in the mix.

Ignorance, successfully fought! :slight_smile:
Thank you all, for the responses to my ‘hijack’.

(My apologies to KarlGauss for ‘questioning his question’.)

Actually, that’s the downward force they experience.

The upward force is the negative of that: weight of fluid displaced minus weight of submerged object.

One way to think about this is that, as compared to other atoms & molecules in the atmosphere, helium atoms get the same push in random directions (due to collisions), but a slightly smaller gravitational force downward (due to lower density). So they tend to migrate upward.

You are basically correct that bouyancy explains helium balloons, but is not a factor for individual helium atoms. In fact, at low altitudes, the distribution of helium atoms is essentially independent of the fact that there are Nitrogen molecules and other gases present. To the first level of approximation, the distribution of helium is controlled by the ideal gas law. The density is greater at sea level because of the pressure of helium atoms above it. If you write down the equations, you find that the rate of decrease of helium density with altitude is proportional to the helium density at that altitude, thus leading to an exponential decline with altitude. This means that there is a certain “half height” at which the density is half as much as at sea level. At twice that height, the density is one quarter as great, etc.

This is true for any ideal gas. The only difference is that each gas will have a different “half height”. The half height is inversely proportional to the mass of the molecule*. For Nitrogen, the half height is about 5 kilometers. A Helium atom is about seven times lighter than a Nitrogen molecule, so it’s half height should be about 35 km.

As others have mentioned, the velocity of lighter gas molecules is higher (inversely as the square root of the mass). This is one of the reasons that Helium can more easily evaporate from the Earth’s atmosphere.

  • The 1/e height h is determined by the altitude at which the gravitational potential energy mgh is equal to the thermal energy kT (k is Boltzmann’s constant). Thus h = kT/mg (with possible multiplicative factors that I’m forgetting.)

This is a really good question, this is my answer:

Firstly in a mixture of gases there will be lots of random collisions which will cause momentum to be exchanged. Consequently the fastest molecules in the gas will tend to be the lighter molecules.

Imagine taking part of the Earth’s atmosphere and putting it in space, where there is no gravity. It will tend to expand and, though all the molecules in the mixture of gases are on essentially random walks, at the leading edge of the expansion there will be more lighter molecules as they are the fastest molecules and are able to get to the edge quicker on their random walks than the slower moving heavier molecules.

The Earth is different in that there are two things that frustrate the expansion of the atmosphere, i.e. everything is subjected to a downwards force and the surface of the Earth acts as a barrier. However if we were to look at it from the point of view of a free-falling frame (ignoring that extended free-falling frames don’t really exist in a gravitational field like the Earth’s), we can see the fact there are more lighter molecules in the upper atmosphere than heavier ones due to the fact that the lighter molecules have the greater ability to ‘out-race’ the heavier ones to get there.

JWT Kottekoe has the right of it.

And just to add, the reason why the lighter molecules tend to be faster: The Earth’s atmosphere is well-enough mixed that all of the various gases in the atmosphere are at the same temperature. Temperature is, basically, a measure of the amount of kinetic energy per particle, so all molecules have the same energy (or more precisely, the same distribution of energies). And since the energy of any individual particle is 1/2 m*v[sup]2[/sup], those with less mass must have more speed.

Outstanding! Your answers have really helped me. I am much obliged.

The idea that lighter atoms or molecules must move faster and are, thus, statistically more likely to go farther in any interval in any direction, also explains why even single atoms/molecules of hot air rise (a process that I might have thought, incorrectly, would have depended on ‘cells’ of warn being formed).

Thank you.

I am pretty sure you were right the first time about this. First of all, it is not really meaningful to say an individual atom or molecule is hotter or colder, and although molecules of hotter air will have a higher velocity, on average, and some of them will have a higher velocity than others, that velocity is not necessarily in an upward direction: it could be downward, or in any direction at all.

Agreed. The average distance a nitrogen molecule moves before colliding with another one at atmospheric pressure is on the order of a tenth of a micron, or ten million times smaller than a meter. Every collision will send the molecule off in an entirely different direction, sometimes up, sometimes down. The faster molecules won’t travel any farther, they’ll just collide more frequently. Also, they will have a different energy after each collision, so they won’t stay “hot” for very long.

They rise like cork and oil float and like hot air tends to get above cold air, without even bringing Archimedes to it. Remember PV=nRT? One of the things we get from it is that for the same volume (be it 1 molecule or 1 cubic kilometer), temperature and amount of particles, a gas with lighter molecules will weigh less than another with heavier molecules; that is, lighter molecules mean lower density. Heavier stuff is attracted by the local gravity (whichever it happens to be) at the same g as lighter stuff, but because F=ma (in the case of gravity, F=mg), the force pulling a heavier molecule down is greater than that pulling a lighter molecule. If you’ll pardon the antropomorphization, the heavier molecules shove the lighter ones out of the way, and out of the way means “up”.