Quantum Mechanics

Remember Bohr? He’s the one with the quantize orbits for electrons It’s a pretty good theory…until you try something besides hydrogen. The problem here is that electrons don’t move in nice, predictable orbits. They don’t have trajectories (the simplest way to think about it is that they teleport from place to place), and they aren’t confined to one little path in space. You can come up with some math to predict where electrons are, though…

Schrödinger Equation We will….not be doing the math. We will, however, use the results.

A Thought Experiment Imagine you’ve just committed some crime, and are out on parole with a GPS tracker. We can take a picture of where you are:

A Thought Experiment 10 minutes later, we take another picture. You’re still at home, but on the other side of the house:

A Thought Experiment Keep taking pictures of where you are, and eventually we see that you’ve left the house, and gone to school:

A Thought Experiment After a while at school, our picture looks like this:

A Thought Experiment After school, you run a few very quick errands, then go home again

A Thought Experiment Repeat all week, and we get a picture something like this:

A Thought Experiment Repeat all week, and we get a picture something like this:

A Thought Experiment Now, imagine that we want to find you, but don’t know your schedule. All we have is this map. We can make a circle around the places we should search, because that’s where you’re likely to be:

Electron Orbitals Electrons work the same way: we can’t follow them and predict where they’ll be. All you can do is take a bunch of pictures, and draw a line around where they’re likely to be. This is called an ‘orbital’. This is an example for one single electron—you look where it is a bunch of times, and when you’re done, you can draw a circle (well, sphere, since it’s 3D) around the nucleus and say “if I want to find this electron, it’s probably inside this sphere.”

Electron Orbitals Not all electrons turn out to have such nice, spherically-shaped distributions, however. In fact, we have to draw two circles here, and say “the electron is probably inside one of these circles, but we don’t know which one.” These two circles represent one single orbital. (Why not one big oval? Because there’s a chunk right down the middle where you never find the electron, so we don’t want to include that bit)

Schrödinger Equation This equation turns out to predict these orbitals very nicely, as well as how many of them there are. We’re going to break them down by size and shape. Size: numbers. 1 is smallest, 2 is bigger, 3, 4, etc. Theoretically there’s no upper limit, but 7 is the maximum we’d currently use. Shapes: given letters as a code

s Orbitals Spherical. Always a single orbital in a given level:

p Orbitals These are the hamburger-buns types from earlier. They don’t start until the second level (2p), and always come in a set of three—along each axis of space. They keep going up and getting bigger—3p, 4p, etc. There is no such thing as a 1p orbital.

d Orbitals These are kinda like double p orbitals. They come in a set of five (pointed various different directions), and don’t start until the third level (3d). (yes, one of them is very funny shaped)

f Orbitals Very large, complex orbitals. Don’t start until fourth level (4f), and come as a set of 7.

All together as a chart shape 1s s 2s 2p i 3s 3p 3d z 4s 4p 4d 4f e 5s 5p 5d 5f 6s 6p 6d 6f 7s 7p 7d 7f Remember, these are not real objects; they’re just theoretical chunks of space where you’re likely to find certain electrons. There is no such thing as a 1s orbital, rather, there are electrons that have a distribution consistent with a 1s size and shape.

The electrons themselves Electrons have one property that’s going to be relevant to using these orbitals: spin. If you take a charged thing and spin it, it acts as a magnet. Which way the magnetic field points depends on which way you spin it.

The electrons themselves Since they have the same charge, electrons already don’t want to be near each other. But they really don’t want to be near each other if they have the same spin, since the magnets line up the wrong way. You repel me

The electrons themselves So, it’s ok to put two electrons in a given orbital, as long as they have opposite spins. The charges still repel, but the magnets attract. Try to put a third one in and…well, don’t try to put a third one in. You’re moderately attractive

So, back to the orbitals s orbitals always came as a single one, so in each given level you can fit two electrons in the s orbital. 1s will hold two, 2s will hold two, 3s holds two, etc. Since p orbitals come as a set of three, you can get up to 6 electrons in them, no matter the size. Following the pattern, d orbitals can hold up to 10 electrons, and f orbitals up to 14.

Summary Electrons don’t live in nice neat, confined little boxes. They go where they want and the best we can do is say “where should we look for them?” Orbitals are a region of space where you’re likely to find a given electron. They come in many sizes (practically speaking, 1-7) and shapes (s,p,d,f). The number of orbitals in a set goes 1,3,5,7 (s,p,d,f). Since each orbital can only have two electrons in it, the number of electrons goes 2,6,10,14 (s,p,d,f).