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the_fungible_man t1_jcx1bsg wrote

One hydrogen atom occupies approximately 6 x 10^(-31) m^(3). Nearly all of that volume is empty space. But then the volume occupied by every atom is overwhelmingly empty space.

The hydrogen nucleus, a single proton at the center, is about 1.7 femtometers wide (1.7 x 10^(-15) m). While the spherical electron cloud surrounding it (which contain one solitary electron) has a Bohr radius of approximately 50 picometers (5 x 10^(-11) m).

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Humble_Cook212 t1_jcwmtr8 wrote

been a while since high school chem but i'll give it a shot - at STP you can have approximately 602,214,076,000,000,000,000,000 hydrogen atoms in 22.4 liters. (molar mass ~1, ideal gas law, avogadro's constant)

throwing the above into some division and algebra, so a single atom of hydrogen would be about a 3.7 nanometers3, at stp.

i'm not sure where I went wrong with the above though, as it doesn't really pass the sniff test - several legit websites refer to the diameter of H being about 0.1nm, and semiconductor manufacturing is currently making silicon features around 20-30nm. so, I'm probably incorrect by an order of magnitude, more than i can explain from my sloppy rounding. you'll get a better answer at /r/chemistry or /r/physics probably.

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lawblawg t1_jcxxbd3 wrote

You're right to do a sanity check; the size of a single atom of hydrogen is definitely not 3.7 cubic nanometers.

Your problem is that you used STP -- standard temperature and pressure -- above. At sea level pressures and temperatures, the gaseous hydrogen molecules (they're molecules, not individual atoms, but that's the least of our problems at this point) have so much kinetic energy that they are zipping around at hundreds of meters per second, constantly bouncing into one another. And so those constant collisions force them to spread out, until they occupy (on average) 3.7 cubic nanometers, even though they are physically infinitesimally smaller.

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Humble_Cook212 t1_jcxyve9 wrote

That makes sense, thanks! I figured the mass/avogadro approach, while extremely useful for lots of stuff, proved not effective here at what I now read to be "what are the electron valence shell diameters". So it seems maybe I answered a question but the wrong question. :) Any thoughts on a different method that would get closer to the published 0.1nm?

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lawblawg t1_jcya1wq wrote

You were on to the right track; you just want to think about it in terms of what's happening at an atomic level. To get as close as possible to the actual physical diameter of a hydrogen atom, you'd want to imagine a situation where the hydrogen atoms were all physically in contact with each other. This doesn't happen in a gas, but it does happen (more or less) in a liquid.

The density of liquid hydrogen is going to vary based on external pressure, but let's start with sea level pressure just to give ourselves a benchmark. The density of liquid hydrogen is 70.85 g/L. I don't even bother doing the calculation with Avogadro's number here; I just asked Google "70.85 g/L = ? amu/nm^3" and it converted grams to atomic mass units and it converted liters to cubic nanometers just fine. The result? The density of liquid hydrogen is 42.67 amu/nm^2. We know that a single hydrogen molecule has a mass of 2 amu, so this suggests that a single hydrogen molecule in a liquid occupies a space of 0.047 cubic nanometers. Solving gives us a radius of 0.26 nanometers. So we can say confidently that a single diatomic hydrogen molecule MUST be small enough to fit within a sphere that has a diameter of 0.52 nanometers.

So how small does that make a single hydrogen atom? Well, you can look up the bond length of diatomic hydrogen and find that it is 74 picometers, or 0.074 nanometers. Covalent bond length is the distance between bonded nuclei, given intersecting electron clouds. So the diameter of a single hydrogen atom must be less than 0.45 nanometers. We're now well within an order of magnitude of the actual size.

Can we do better? Yes, we can, by looking once more at what's actually happening at an atomic level. Think about a ball pit: there's a lot of empty space between the actual individual balls. Being (essentially) spheres, hydrogen molecules don't pack into each other perfectly; they leave space in between each other. How tightly can you pack spheres together? This is a well-studied problem. In a perfectly hexagonal offset lattice, spheres can be packed with an average density (relative to the space between them) of π/3*2^0.5 or ~0.7405. That would be if the hydrogen molecules were arranged in a perfect crystalline structure. Unfortunately, hydrogen molecules are nonpolar so they don't have any intermolecular electromagnetic forces to align them that way; they will be packed randomly. This is called a random close pack and mathematicians have found that such irregular packings will produce a density of 0.64 or thereabouts.

What does this tell us? Well, if the density of liquid hydrogen is measured at 42.67 amu/nm^2, but the molecules are only packed to a volumetric density of 0.64, then 36% of that volume is going to be empty space. So the actual density of an individual hydrogen molecule is 66.7 amu/nm^2 or 0.03 cubic nanometers per molecule. This gives me a radius of 0.193 nanometers. Subtract the bond length and I get a diameter of 0.238 nanometers for a single hydrogen atom.

The actual size of an atom is known as the van der Waals radius. The van der Waals radius of a hydrogen atom is 1.09 angstroms or .109 nanometers. So the actual physical diameter of a hydrogen atom is 0.218 nanometers.

So our approach got us within 10% of the real number. Not bad!

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Traditional_Cat_60 t1_jd0qpxy wrote

Most of that 22.4 L of space is empty space, not atoms. The 22.4L/mol at STP is the volume the gas takes up, including all the empty space in between them . It is not the volume of the atoms themselves. Compared to the 22.4L, the atoms themselves take up a very small amount of the volume.

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DudeWithAnAxeToGrind t1_jcx5ook wrote

At the beginning, there were no atoms, because densities were too high for atoms to exist. It was some weird quantum soup of particles.

Also, not sure where you are going with knowing the size of hydrogen atom. You can't simply pack those as tight as possible. As you pack those hydrogen atoms more and more tight, at some point protons will capture electrons, turn into neutrons (and release neutrino in the process). This is how neutron stars form. Neutron stars are about densest you can get matter before it collapses into a black hole.

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ExtonGuy t1_jcxpp1d wrote

The diameter is about 0.21 nanometers. That’s how close they pack under standard conditions.

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EdPeggJr t1_jd08lf1 wrote

Start with a neutron. In about 888 seconds, it'll unpack into a hydrogen atom.

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EntropicallyGrave t1_jcwy1c4 wrote

A good thing to consider is when they formed; look at what the big bang people say the size of the universe was when the CMB formed, and divide. Otherwise I'm not sure the question will ultimately be easy to well-define. (But I don't know this stuff)

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Alvsvar OP t1_jd63wnf wrote

Danm, that was one hell of answer thanks for the info although the units are abstract for me and I can't even remember Avogadro's law . Im probably getting this wrong but does this mean in 22.4 l of empty space there is one hydrogen atom? Thats super interesting how little hydrogen is in an atom, those strong nuclear forces.

The reason Im asking this is I was wondering if you could have a "net" that could collect these and other atoms, for a space ship. I was also interested how much hydrogen was there and how empty it really was. Its so crazy these coalesce into everything that built the universe.

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EntropicallyGrave t1_jd6bxpc wrote

I was downvoted a bit, but the top answers are acting like atoms just "end" at some point; I mean, the answer they give, I'm guessing, would be just about right - but my point is that it is a sort of a "functional" definition... they are, in some sense, processes - atoms. Or events.

u/DudeWithAnAxeToGrind is saying good things; it's about when you decide it no longer looks like a "quark-gluon plasma" to you, and when it looks more like atoms. we don't even understand how water works, if you start looking at it close, like that

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Alvsvar OP t1_jd9ceft wrote

Now Im going to down vote you! Just kidding its funny how personal folks take that.

Yea I see planets and moons orbiting them, or solar systems galaxies, or galaxies black holes. How you can predict when they will be at a certain point even thought we dont see them. Then an atom with its electrons orbiting them, how fare does it go? And all thats mostly a vacuum, oh but wait

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EntropicallyGrave t1_jda6rvo wrote

The things we think of as "observers" are extremely complex - so we're proposing something very restrictive, when we propose that we might understand physics. We're saying that there are no artifacts of this relationship that blind us.

It's important to be aware of the known mechanics of electrons; they don't move at all like classical objects; but it is their motion from which classical motion emerges, in some sense, too

It is almost arbitrary, whether you discuss things as a space populated with stuff, or if you just discuss the stuff and its relationships with itself; the nature of space is one of unreality.

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