Atoms: I need the Straight Dope!!!!

Factual Questions
1

I used to be quite a firm believer in the theory of atoms until I started to ponder these questions…

I know that the electron of an atom is an extremely long distance from the nucleus in proportion to its size. Knowing this, what exactly exits between the spaces of the electron cloud and the nucleus?

And if there is so much space in between the nucleus and the electron cloud, couldnt other atoms just pass right through?? If thats true should you be able to pass your hand through a desk?

I got a kinda partial answer to that and it had something to do with the positive and negative charges of the particles, but couldnt you still do it? Also, why do electrons prefer to orbit the nucleus in fields of 8 (and the first field of 2)??

These questions really mess with my head!!!

2

okay, I have an understanding on why these are not possible, but I am not to person to explain it. So to the top this goes and hopefully you can get a better explination that my blabbering three years after my physics class can do for ya.

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3

Bohr orbits (the 8 shells theory) has been disproved.
It is still taught as a good way to visualize the atom but it has no relationship at all to how an atom actually exists. Bohr theory explains how the energies and binding affinities of the electrons can be related.

In fact it is quite difficult to explain how things operate on a quantum level. The space that electrons occupy must be undestood in tems of a probability cloud.

At a slightly more than elementary level you might be intorduced to orbits that look like intersecting figures of 8. These orbits are said to descirbe the probablity of finding a particular electron in that area. The fact is that at any one particular poin tin time the electron could indeed exist very far removed from the confines of even these orbits.

Thanks to the theories of Edwin Scrodinger et al we understand a little more about how things look. Unfortunatly there is a paradox that means that the harder we try to see an electron the more we are changing it from its natural state.

Theories on how an atom looks are many and varied and work continues in this area. The most recent computer modelling has produced images of a fascinating energy Bank or Wall around the “orbits”. i understand the follows IBM are doing new work in these area as they attempt to step us twoard a better understanding and consequently quantum computing. (http://www.almaden.ibm.com/vis/stm/images/stm.gif)

(http://www.almaden.ibm.com/vis/stm/images/stm15.jpg)
To awnser your questions you must first unsderstand the tangibility of the interstitial space between the electrons. At the quantum level our theories about how matter exists and operates are basicaly out the windows. It is wrong to attemt to visualise the atom in purely physical terms because thats is simply not possible.

To get you started http://www.sr.bham.ac.uk/xmm/fmc2.html

4

The charges on the electrons of each atom repel each other. To get an idea of how this works, try taking two powerful magnets, and hold them so that the like poles are near each other (yes, of course I know that polarity isn’t the same thing as charge, but the large-scale effect is similar). Now push them together. You’ll probably be able to do it, true, but it takes some work. In the case of atoms and trying to move your hand through your desk, it would take so much work that the desk and/or your hand would be knocked to pieces long before you’d get them to overlap. The space between electrons and nucleus isn’t exactly empty; it’s full of electric and magnetic fields. They’re not matter, perhaps, but are very significant, nonetheless.

As to the arrangement of electrons in various energy levels, I have no clue how to explain it without at least six months or so of quantum mechanics. Any of the other resident physicists want to give it a shot?

5

Atoms can be characterized by four variables, representing such things as energy level, orbital shape and spin. As the energy level increases, the electron has a greater chance of being far from the nucleus. If you want, I would be pleased to cover this in far greater detail. It’s very important both in courses I took in organic chemistry and quantum physics, but irrelevant to the OP.

When you slap a desk, you ARE cutting through some desk electrons a long distance from their nuclei. But your hand stops when it reaches a place where the “desk” atoms are sufficiently dense and close together. One visual aid, more accurate in metals, is a regular grid of nuclei with a sea of electrons. Different substances have different visual aids, but gases have the atoms more widely spaced than solids. You can slap the air all you please because the nitrogen and other gases are widely separated.

6

Chronos said:

Me neither. A detail-less answer, though: there is a jump in energy each time you go past a filled shell.

When you add an electron to an atom, it has to go into a quantum mechanically allowed “state” (everything is in a “state”). If you were to list the allowed states for electrons in order of increasing energy, you’d find that they lie in groups. There is a cluster of two states near the bottom, then a cluster of eight a little ways up, etc. (the cluster of eight is really more like another cluster of two and then a cluster of six, but they’re close enough to call one cluster of eight for our purposes.) Furthermore, if you add an electron to an atom, it can’t go into a state that already has an electron in it. If there are any electrons roaming around looking for a home, they will pick the home that will result in the lowest energy for them. If an electron tries to add itself to a noble gas (like neon, with 10 electrons), it will be forced to live in the 11th state – that high energy 11th state, past the first two clusters. But, if it finds fluorine (which has 9 electron), it gets to be the 10th one, so it gets to live at a lower level, down in that cluster of eight. (And thusly, fluorine is reactive; Neon is not.) These clusters are often called shells, and chemists (and others) speak of the shells as being “filled” as you move across the periodic table.

The question, then, becomes why are there 2 and 2 and 6 and … states in each shell. This is the harder part. What the heck. I’ll see what comes out. It’s long, so you’ll have to bear with me…

Since we don’t have those six months to learn some quantum mechanics (QM herafter), I will just claim some things.

  • Angular momentum comes in two types, spin and orbital. Call the total orbital angular momentum L. The square of L can only take on values of the form l*(l+1)*(a constant) with l being any positive integer (1, 2, 3,…). (That’s an italics lowercase “L”, BTW, in case it’s not clear in your font.) The important point in this dense paragraph is that we can index the possible values of total orbital angular momentum by this l thing. We can say, “Our state has l=2.” l can be any non-negative integer.

  • You need more than just l to specify a state, though. There are a whole slew of states with a given l. You can further identify a state by its angular momentum along one given axis. Notice the above quantity (L) was the total angular momentum. We can ask how much of that is along one axis (but only one – QM doesn’t allow you to specify the angular momenta along two different axes at the same time!) We can similarly index the allowed values of this quantity by an integer. Let’s call it m. Turns out that m can take on values from -l to l (integers only).

  • There’s still more! An l and an m together is still not enough to fully say which state is which. An electron has a certain probability of being here or there. If you give me an l and an m, it turns out you’ve given me information about the angles at which I can expect to see the electron if I was sitting at the nucleus looking out. I still need information about how far away the electron is likely to be (angles aren’t enough) if I want to have a guess at where it is (i.e., if I want to specify the state.) This “distance” quantity can be indexed by an integer, too. Let’s call it n. Turns out that n can equal any positive integer above l.

  • One more! The electrons can have two values of spin angular momentum (or simply, spin). We can obviously index this by an integer. Call it s. It can equal 1 or -1 (by convention).

Whew! So, if you give me an l, an m, an n, and an s, you have specified a state, and no two electrons can have the same values for all four of these “quantum numbers”.

Back to energy… You can work out an expression for the energy of a given state. Once you’ve done that, I can say, “How much energy does state (n, l, m, s)=(1,2,-1,1) have?” and you can go to your formula and say, “This much!” If you do this, you’ll find these facts:

  • Changing n changes the energy a lot.
  • Changing l changes the energy a lot.
  • Changing m doesn’t.
  • Changing s doesn’t.

So we can now see our clusters (shells) taking shape. Since n and l have a big effect, all the states in a given cluster have the same values for these. If we want to know how many states are in each cluster, we need only ask how many states have the same n’s and l’s. In order of increasing energy:

- n=1, l=0.
m can take on values -l to l, or simply 0. s can take on its two values. Thus, there are two states with n=1, l=0.

- n=2, l=0.
m can take on values -l to l, or simply 0. s can take on its two values. Thus, there are two states with n=2, l=0.

- n=2, l=1.
m can take on the values -1, 0, and 1. s can take on its two values. 2 times 3 equals 6 possible states. Thus, there are six states with n=1, l=0.

And so on. It turns out that the jump in energy from an l=0 state to an l=1 state isn’t that big, so the two and six states are often viewed as a single eight-state shell. Doing this means that l doesn’t matter anymore, and all you need to do is know n to know which shell you’re in. A different way or wording this: n affects the energy most of all.

I really should proofread this, but it is late. I am tired. Apologies.

7

A fully accurate post, Pasta, although I’ll leave its understanding as a matter to be judged by someone who doesn’t already know QM. One thing I would like to clarify, though:

This means that changing m or s doesn’t change the energy a lot, not that it doesn’t change it at all. They’re responsible for what’s called fine and hyperfine structure, respectively, with slight changes in the energy for each.