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Old 05-02-2008, 11:57 AM   #16
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Re: Why are atoms round(or are they?)

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Also - and I'm talking out my ass here a little bit - for the larger atoms where the weirdo orbitals start coming into play, I'd think the overall size and shape of the atom would be dominated by the lower filled n states. Once you fill all of the orbitals of a particular angular momentum I'm pretty sure you must recover spherical symmetry, and so if those are responsible for the bulk of the size, then whatever deviations from roundness you have from last orbital seems like they would probably be relatively minor.
Well, the "shape" of the overall atom would probably correspond to its largest (outermost) orbitals. And those would be for its highest n state. So this reasoning is probably not correct.

The "weirdo" orbitals are of much higher energy, so the highest filled shell never contains them (only s and p orbitals). Palladium may be an exception. At any rate, the electron distribution doesn't always resemble a sphere.

Also, orbitals don't really represents a "shape." There are no "boundaries" to the orbitals, and the boundaries typically drawn are based on an arbitrary percentage (usually 90%) that an electron will be found within the region. Electrons can move outside of the region, sometimes so far outside of the region that they leave the atom and become part of a different atom ("tunneling"). I'm not sure how quantum weirdness factors in, but I'd bet atoms don't really have "shapes" per se, and that if they did they would represent fluctuating "blobs" more than spheres.
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Old 05-02-2008, 01:49 PM   #17
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Re: Why are atoms round(or are they?)

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Also, orbitals don't really represents a "shape." There are no "boundaries" to the orbitals, and the boundaries typically drawn are based on an arbitrary percentage (usually 90%) that an electron will be found within the region.
Right, but come on, this represents a shape. To say that the shape represents a rigid object like a block or something is obviously wrong, but one can easily talk about the shape of the distribution, which is what is pretty clearly meant there.

Also,

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Well, the "shape" of the overall atom would probably correspond to its largest (outermost) orbitals. And those would be for its highest n state. So this reasoning is probably not correct.

The "weirdo" orbitals are of much higher energy, so the highest filled shell never contains them (only s and p orbitals). Palladium may be an exception. At any rate, the electron distribution doesn't always resemble a sphere.
you're right on the second one, but I feel like this is more of an argument for why you'd expect them to be roughly round (higher l states do tend to push out away from the center for centrifugal reasons, but I think higher n's push out too.) My point with the nesting and large n is that even if you did have some of the weirder orbital shapes, because there's a substantial spherically symmetric core, the proportional deviations from roundness are probably smaller than you'd expect looking at just the shape of the valence orbitals. EDIT: In other words, it would be the difference between a cigar and a ball with some bumps on it.
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Old 05-02-2008, 02:09 PM   #18
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Re: Why are atoms round(or are they?)

Agreed on all counts. I should have said they don't have a definite shape, not that they don't have a shape. "Ball with bumps" is how I'd visualize it. But in terms of the OP, I would consider that more of a "they arrange themselves in random shapes and we just depict them spherical." It's a bit semantic, but I think it's important to note that this is more complex than gravity (partly because tiny particles are weird, partly because there are repulsive forces involved, partly because electrons need to be in motion/can't be confined to a specific position).
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Old 05-02-2008, 03:08 PM   #19
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Arrow Re: Why are atoms round(or are they?)

Particles take the path of least resistance. A sphere is--for electrons at least--the shape in which they will usually be found when in their least energetic state. While I hold no advanced degree in chemistry, I have heard that there is evidence that suggests the presence orbitals like this within the nucleus as well.

But anyway, atoms usually have so many orbitals around them that they're never round. Hydrogen, yeah, but that can't hold any more electrons. In chemistry textbooks, you'll find that p and s orbitals for example are very different looking. My organic prof had beef with this, as one poster has already spoken about...they don't look very different IRL. I would imagine that an atom always strives to be as spherical as possible, given that a sphere is the easiest shape to be in.
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Old 05-03-2008, 11:33 AM   #20
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Re: Why are atoms round(or are they?)

It seems like over a time average, with a large number of electrons, the atom must be quite close to spherical, just to minimize potential energy, no? Doing anything different would seem inefficient, and I just don't know what forces would create such a lack of time-averaged spherical symmetry.
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Old 05-03-2008, 01:25 PM   #21
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Re: Why are atoms round(or are they?)

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It seems like over a time average, with a large number of electrons, the atom must be quite close to spherical, just to minimize potential energy, no? Doing anything different would seem inefficient, and I just don't know what forces would create such a lack of time-averaged spherical symmetry.
The problem is that electrons are attracted to the protons, but they are also repelled by one another. For a single electron, and even for a pair of them, this isn't all that complicated. But when you have more electrons involved, these attractions and repulsions start having patterns.

The patterns can be described using a nasty bit of math called a "wave function," and they can be experimentally observed (to a degree). After looking at atoms and crunching the numbers, we see that the electrons tend to exist in specific regions most of which are not spherical, because that minimizes the potential energy better than simple spherical orbits. The way it works is related to stuff like the wave nature of the electron, and it gets funky, but it all adds up to specific types of repeating orbitals.
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Old 05-03-2008, 05:38 PM   #22
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Re: Why are atoms round(or are they?)

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It seems like over a time average, with a large number of electrons, the atom must be quite close to spherical, just to minimize potential energy, no? Doing anything different would seem inefficient, and I just don't know what forces would create such a lack of time-averaged spherical symmetry.
The higher orbitals usually look like hourglass shapes.
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Old 05-03-2008, 10:07 PM   #23
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Re: Why are atoms round(or are they?)

Atoms are generally round in shape for practical purposes. The whole field of crystallography is based on this model and its predictions are very accurate (i.e., estimate the theoretical density of a material using the crystal structure and the atoms touching as hard spheres and it matches the actual density). Look at a plane of atoms using atomic force microscopy and you can "see" the atoms which resemble the hard sphere model.
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Old 05-03-2008, 10:12 PM   #24
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Re: Why are atoms round(or are they?)

The orbits of electrons must satisfy the Schrodenger equation. The solutions to the schrodenger equation with a central electric potential are products of angular distributions and radial distributions. The angular components form the shape in discussion. The solutions to the angular part of the three dimensional Schrodenger equation are called spherical harmonics and can take many shapes.

The potential that binds the electron to the nucleus is spherically symmetric. In other words, it pulls equally in all directions without any preferred direction. This is why spherical harmonics come into play.

Spherical harmonics aren't always spherical. They have many shapes each with different values of angular momentum. The "S" states are spherically symmetric. "P" states have total angular momentum 1 and are not spheres, rather they look like weird bulges coming out of the proton.

To agree with what has been said earlier, the electron orbitals are wavefunctions. They don't describe the shape of the electron's orbit, but rather they describe the probability distribution of the electron. They are defined over all space, but have maxima at certain radaii and angular distributions. It is the contours of equal probability which we describe as having a particular shape.
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