
Why do electron shells have set limits? (1999) - xingyzt
http://www.madsci.org/posts/archives/1999-03/921736624.Ch.r.html
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saurik
I feel like this answer is "no, there is no reason for that to be the sequence
you are seeing: it is an accident, as you can see from this careful analysis
which demonstrates exactly why it is that sequence"... it is like saying "I
noticed a bunch of random processes fall into a normal curve, is there a
mathematical reason for that?" and saying "oh no, that is entirely on
accident; here, let me show you the math for how a particular kind of random
selection causes that exact distribution you are seeing, along with the
equations that characterize if... as you can see, no math is involved here:
this was just an accident" :/.

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hinkley
In this vein, I really enjoyed 1brown3blue breaking down why prime numbers
form patterns when graphed in polar coordinates.

[https://youtu.be/EK32jo7i5LQ](https://youtu.be/EK32jo7i5LQ)

~~~
chadcmulligan
That is one of the most artistic expositions of mathematics I have ever seen.

~~~
stallmanite
3blue1brown is most likely the greatest math teacher alive. I’ve looked far
and wide and found nobody who competes. Any HN’ers have suggestions for other
math educators working on his level?

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nullc
It always seemed natural to me that the number of electrons would grow
quadratically with the distance (principal atomic number), just like the
surface area of a sphere grows quadratically with increasing radius.

I feel like the author of the comment calling it "by accident" would be
extremely unhappy with number theory. In number theory all sorts of properties
seem to crop up "by accident" but turn out to have incredible consequences and
you realize that virtually every "accident" couldn't have gone any other way
without destroying all of mathematics.

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whatshisface
The electron shells themselves are in reality 3D objects _that go all the way
to the center_ , so it is a little strange after all that it increases with
the surface area.

~~~
number6
Is this true? I mean its a model. Aren't electron shells the quantum states of
the electron fields?

~~~
thicknavyrain
It is true. The classical wavefunction of a ground state electron overlaps
pretty heavily with the nucleus of an atom IIRC.

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jeherr
Only for s-orbitals. Anything with a quantum number l>0 has 0 probability at
the nucleus.

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Crazyontap
Forgive me for posting this idiotic question in advance since I have very
little knowledge of physics, but I have often been confused about one thing
recently. From what I could gather a little isn't the whole electrons revolve
in orbits thing proved false and outdated like universe is made of ether?

I heard that even the iconic atom logo is all wrong since it is proved that
electrons don't revolve around anything rather come in and out of existence
and present themselves in probability clouds. If that is true then why do we
still keep talking about shells and energy levels?

Like I said my question may sound like a troll but I assure you it's not. Just
want to know what's what.

~~~
madhadron
You are correct, the Bohr model has been obsolete for almost a century. It
continues to get trotted out because the more accurate model is quite
unapproachable without a lot of math and study.

When someone says "revolves around something" they are mentally projecting a
whole sequences of measurements of the electron's position, one after another,
that trace out a path. We are evolved to regard the path as a natural thing as
opposed to focusing on the measurements.

But we can't do that for electrons orbiting an atom, since measuring them
involves wacking them with photons or something that bounce off in some
direction so we can see that deflection. So all we get to talk about is the
result of a measurement.

When someone says "it's in this orbital," that's a statement about the values
of energy and angular momentum a measurement will produce. What measurements
actually produce those? Ones that involve absorbing or emitting photons,
mostly, and we measure those by the energy of the photon absorbed or emitted,
and those don't give us information about the position of the electron. You
may think that we could put an electron into a very high orbit and then try to
triangulate where it was when it emitted the photon based on the angle...but
then you have to know where the atom is precisely, which means another
measurement, which means some unknown momentum imparted, which means the
energy spectrum of the photon we're trying to measure gets smeared...

Meanwhile, if we measure position precisely, then we impart some new momentum
vector to the electron. What the momentum vector would have been measured to
be before that wasn't known, and so we have no idea how we have kicked it and
the orbital (energy and angular momentum) can have various values if we
measure them afterwards even if they would have always had a single value
beforehand.

~~~
vertbhrtn
Is the accurate model that complex, though? An electron is a standing wave:
one could show the first two standing waves on a drum and say these are the
lowest two electron energy levels. Higher levels create more sophisticated
waves, and non-flat potential adds more complexity, but the idea remains the
same.

~~~
madhadron
An electron isn't a standing wave, so apparently it is that complex. :(

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vertbhrtn
What is it then?

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madhadron
It's own thing, and thinking of it as a classical wave or a classical particle
isn't accurate. You go through the math and the experiments and try to build
and intuition for what it is in its own right without reference to classical
analogies.

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avalys
This is such a classic physicist’s answer. It starts off promising, with a lot
of context and detailed exposition which leads one to hope that perhaps it
will be pulled together into an enlightening explanation at the end.

But when one reaches the end, one finds merely the truism “It is this way
because that’s what you get when you solve the equations.”

(yes, I have spent a lot of time working with physicists.)

~~~
aeternum
You're right. The way to explain it intuitively is that at the quantum scale
all particles are wavelike.

In order for electrons to achieve stability (such as within an atom), they
must create a standing wave. Similar to the notes on a guitar string, each
electron orbital is simply a harmonic.

The complication comes from the fact that atoms are 3d, so instead you need to
use spherical harmonics, but it's the same principle, just standing waves in
3d space. These should look familiar if you've seen rendered images of
electron clouds:
[https://en.wikipedia.org/wiki/Spherical_harmonics](https://en.wikipedia.org/wiki/Spherical_harmonics)

It is quite surprising that this intuition is basically never taught in
classrooms.

~~~
guerrilla
Thank you. That makes much more sense to me. I found this[1] video with an
efficient explanation and visualization.

[1]. [https://youtu.be/Ziz7t1HHwBw](https://youtu.be/Ziz7t1HHwBw)

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matthewfcarlson
Not sure what this says about me, but before I looked at the year I thought
this was about electron apps as command shells

~~~
kfarr
I was thinking like wow electron has been around a lot longer than I thought!

~~~
mattigames
Or from a different timeline where its 1999 and you can create electron apps
by bundling them with ActiveX and Internet Explorer 6 _~shivers~_

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matthewfcarlson
Yeah- it's not a pleasant thought. It's like some horrible episode of twilight
zone made just for developers.

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tmsh
There's a series I've enjoyed recently:
[https://www.youtube.com/watch?v=zKbZeUvPnWI&list=PLpH1IDQEoE...](https://www.youtube.com/watch?v=zKbZeUvPnWI&list=PLpH1IDQEoE8Q8842yVe-V8m7PN-R9rlwi)

"How Small is it" by David Butler. Offers a nice summary of electrons and goes
deeper into the Higgs field.

My two cents - after watching it - is it could all (i.e., wave/particle
duality of electrons) be explained a lot more clearly if we just accept there
is another dimension in space that electrons move into and out of, which we've
not yet figured out how to observe.

Would explain dark matter / dark energy a lot too. The model seems so
incredibly simple to me that I just don't get why more people haven't tried to
build on it (am so busy with other stuff I doubt I'll have the time to figure
out unexplained Cosmological or other phenomena that could be better explained
by this model).

But it seems really straightforward this way. Electrons are small enough,
independent enough to move out of and back into another magnitude of space
that we can't measure. To us in 3-space it looks like they leave and come back
(the idea of a particle being a "wave with itself" is less clear if you ask
me). Everything is particles, it's just some particles have axis of motion in
space that we don't know how to perceive yet.

One can think about it by analogy. Suppose we all lived in 2 space. If
particles in 2 space where small enough to detach from our plane and pop up
and down above and below the plane they would seem to appear and disappear.

It's the same thing with 3 -> 4 space. At some point people will realize that
thinking about space as 3 space only is like thinking that the world is the
center of the solar system. Our three dimensions are simply the closest / most
defined / perceived ones to us. They're not even the "central" ones. They're
the closest one's to our perception / how we've evolved.

If you get into the smaller spaces of things, there's less binding energy that
constrains matter and more flexibility in moving between other dimensions.
Likely there's a major 4th dimension that matter moves through / oscillates if
you prefer since it's smaller particles that move the most (though
cosmologically we see the effects in the large). And likely once you get deep
in the 4th, there's a fifth, etc.

Again the analogy from "Flatland" / 2d space is you don't realize the freedom
to move into 3 space until you separate yourself from the structure of what
Flatland is made of at the sort of macro level. For us in 3 space the macro
level is atoms. As you dive deeper inside, you're not bound by these
constraints.

Gravity, everything can be modeled as particle forces if you just realize
there's dimensions we don't perceive at the macro level yet (but which can be
perceived indirectly by their effects on our 3 space - just as in time you can
figure out what something moving in and out of a plane is sort of doing in 3
space).

~~~
Kednicma
How would you reply to the Kochen-Specker Theorem [0] (or its consequence, the
Free Will Theorem)? The main problem with treating subatomic particles as tiny
spheres, rather than as waves, is that we immediately have problems with
entanglement and Bell's inequalities. I would be interested in hearing how
you're going to handle that.

[0]
[https://en.wikipedia.org/wiki/Kochen%E2%80%93Specker_theorem](https://en.wikipedia.org/wiki/Kochen%E2%80%93Specker_theorem)

~~~
tmsh
Thanks for the question and the link.

My sense is that being able to move through other dimensions (specifically a
fourth spatial dimension) and into/out of our 3 space happens ‘superluminally’
since it’s more or less instant. The speed of a particle in 3 space has no
dependence on its speed in the 4th dimension (by analogy with flatland - the
speed at which a particle on the plane moves out of the plane).

No reason to assume the 4th dimension is constrained by the speed of light. I
guess I don’t know enough about Bell’s inequalities and entanglement (yet!
Will look forward to reading more) but I think that might help. A fourth
spatial dimension is both local and nonlocal (it affects particles at all
points in 3 space but isn’t constrained by 3 space). And it makes sense that
it shows up only when we get down into the fabric of 3 space (subatomically)
since...honestly am still trying to figure that out.

Is our 3 dimensional “flatland“ hurling through 4 space really fast? Are we
suspended like with a magnet on both sides of our flatland, holding particles
in place - except for leptons and photons which can oscillate above and below
the plane?

Is the many worlds hypothesis true? Do we mostly move through 4 space on an
arrow of time? And there’s a clear inertia there. But at the edges we can move
through other 3 spaces? Why is there such inertia? How do we not be totally
bound by it and move without its constraints?

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dboreham
Because those are the values specified in the simulator's .ini file?

I suppose they probably upgraded to a .yml file recently..

