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Bl-zUmeYj74-008|Electrons are charged, and if they spun around their axis, they would create a tiny magnetic field. |
Bl-zUmeYj74-009|Now, electrons undoubtedly don't spin about the axis. |
Bl-zUmeYj74-010|They might not even have an axis. |
Bl-zUmeYj74-011|No one has ever seen an electron. |
Bl-zUmeYj74-012|It's one of the interesting parts of science. |
Bl-zUmeYj74-013|No one has ever seen one of those things. |
Bl-zUmeYj74-014|We don't know what it looks like. |
Bl-zUmeYj74-015|But the electron has a property that behaves like it's spinning around an axis. |
Bl-zUmeYj74-016|Remember when we had photons, and they behaved like they had momentum? |
Bl-zUmeYj74-017|The photons don't have mass, so they can't really have an MV momentum, but they have a property that behaves just like momentum, that photon energy. |
Bl-zUmeYj74-018|Same thing with electrons. |
Bl-zUmeYj74-019|They probably don't spin about an axis, but they have a property that behaves just like an electric charge spinning about its axis. |
Bl-zUmeYj74-020|So if a electric charge spins about an axis, it acts like a little magnet. |
Bl-zUmeYj74-021|So here I have a little magnet. |
Bl-zUmeYj74-022|Let's look at that. |
Bl-zUmeYj74-024|So here's a little bar magnet. |
Bl-zUmeYj74-025|If it's in a magnetic field or not in a magnetic field, depending on when I bring this magnet in, that will determine the properties of this little bar magnet. |
Bl-zUmeYj74-026|Let's take the magnet away right now. |
Bl-zUmeYj74-027|It's in no magnetic field. |
Bl-zUmeYj74-028|So it can point in any direction in space. |
Bl-zUmeYj74-030|Just like an electron, it has a preferred direction in a magnetic field. |
Bl-zUmeYj74-031|Here's a low-energy direction aligned with the magnetic field. |
Bl-zUmeYj74-032|If I push it away from that low-energy direction, I have to put energy in. |
Bl-zUmeYj74-033|And if I release my finger, it'll go back to the low-energy direction. |
Bl-zUmeYj74-034|This little bar magnet can point in any direction with respect to the field. |
Bl-zUmeYj74-035|I can give it any amount of energy and have it spin back to its preferred direction in the magnetic field. |
Bl-zUmeYj74-036|For electrons, that direction in the magnetic field is quantized. |
Bl-zUmeYj74-037|It can only be spin up with the magnetic field or spin down against the magnetic field, quantized energy levels, two of them. |
Bl-zUmeYj74-038|And we're used to quantization now for tiny particles. |
Bl-zUmeYj74-039|So we understand electron magnetic field can't point in any direction. |
Bl-zUmeYj74-040|It can point spin up or spin down. |
Bl-zUmeYj74-041|Let's look at an experiment that manifests that. |
Bl-zUmeYj74-042|If you take electrons and you send them through an inhomogeneous magnetic field, they will separate based on their spin. |
Bl-zUmeYj74-043|Out here, where there's no magnetic field, they can either be spin up or spin down. |
Bl-zUmeYj74-044|As they pass through the magnetic field, that will sort them based on whether they're spin up or spin down. |
Bl-zUmeYj74-045|Now, if they could point anywhere with the magnetic field, you'd expect them to go through the magnetic field and just end up any old place. |
Bl-zUmeYj74-046|The ones that were pointing slightly up would go high. |
Bl-zUmeYj74-047|The ones that were pointing slightly down would go low. |
Bl-zUmeYj74-048|The ones that were pointing in the middle would go straight. |
Bl-zUmeYj74-049|But we know that the electron spin is quantized. |
Bl-zUmeYj74-050|It can only be spin up or spin down. |
Bl-zUmeYj74-051|So when you do this experiment, you get a group of electrons, the ones that were spin up and give you a bright spot here. |
Bl-zUmeYj74-052|The ones that were spin down give you a bright spot here. |
Bl-zUmeYj74-053|Two possible orientations of the magnetic field for electrons. |
Bl-zUmeYj74-054|So we're going to call this property of the electrons. |
Bl-zUmeYj74-058|Plus 1/2 and minus 1/2 will be the spin values for the electron spin. |
Bl-zUmeYj74-059|So that's another quantum number. |
Bl-zUmeYj74-060|So we have n, l, m sub l that defined the orbital. |
Bl-zUmeYj74-061|And now we have m sub s, which defines the spin of the electron. |
Bl-zUmeYj74-062|So four possible quantum numbers now can describe an electron about an atom. |
Bl-zUmeYj74-063|N, l, m sub l, and m sub s. |
Bl-zUmeYj74-064|Now, it's interesting. |
Bl-zUmeYj74-065|This quantum number has a half integer value. |
Bl-zUmeYj74-066|All the other quantum numbers have this integer value of 0, 1, 2, minus 1, minus 2, etc. |
Bl-zUmeYj74-067|Now we have a half integer value. |
Bl-zUmeYj74-068|And you may wonder why that is. |
Bl-zUmeYj74-069|Well, it has to do with the strange properties of electrons. |
Bl-zUmeYj74-070|Electrons are crazy little particles. |
Bl-zUmeYj74-071|Like I said, no one has ever seen one, so we don't know what they look like. |
Bl-zUmeYj74-072|But they have strange properties that don't behave like normal particles. |
Bl-zUmeYj74-074|And that's kind of odd right? |
Bl-zUmeYj74-075|Usually expect something-- if you say, I'll take this and I'll go around in a closed loop, it should look the way it looked when it started. |
Bl-zUmeYj74-076|Electrons don't behave that way. |
Bl-zUmeYj74-077|They have a twist in their space relative to our space. |
Bl-zUmeYj74-078|And they act kind of like this device here. |
Bl-zUmeYj74-079|This is a Mobius strip. |
Bl-zUmeYj74-080|This has a twist in its space relative to our space. |
Bl-zUmeYj74-082|I have to go around this loop twice to get back to the same state that I started in. |
Bl-zUmeYj74-083|That's how electrons behave in our space because their space is twisted relative to ours. |
Bl-zUmeYj74-084|They're very, very crazy little particles. |
Bl-zUmeYj74-085|We're going to look at now taking those electrons and placing them into orbitals more than one at a time. |
Bl-zUmeYj74-086|So we're going to move beyond the hydrogen atom to the rest of the elements of the periodic table and look at multi electron atoms. |
1qiwlqrG6VY-000|I can form molecular orbitals from atomic orbitals by taking linear combinations of atomic orbitals. |
1qiwlqrG6VY-001|I can add them and subtract them with constant coefficients. |
1qiwlqrG6VY-002|So my atomic orbitals, when I'm talking about the p orbitals can be added and subtracted, I have to choose an internuclear axis though. |
1qiwlqrG6VY-003|So I'm going to choose the internuclear axis, the axis that contains both nuclei, as the positive z-axis. |
1qiwlqrG6VY-004|If I choose the positive z-axis, then I can add the pz orbitals together, pz atomic orbitals to form a molecular orbital. |
1qiwlqrG6VY-005|Now notice I'm going to add these two orbitals, but look how the signs overlap. |
1qiwlqrG6VY-006|Remember, red and green represent opposite signs. |
1qiwlqrG6VY-007|Green can be positive, red can be negative. |
1qiwlqrG6VY-009|So I'm going to bring those two together and make that linear combination. |
1qiwlqrG6VY-010|I choose that linear combination because that gives me a higher amplitude, a higher probability of finding electrons, between the two nuclei. |
1qiwlqrG6VY-011|Constructive interference between the two nuclei leads to a bonding orbital. |
1qiwlqrG6VY-014|I can show you that with these little models. |
1qiwlqrG6VY-015|Here comes one atom with a pz orbital and another atom with a pz orbital. |
1qiwlqrG6VY-016|Multiply this one by negative 1, so that I get constructive interference. |
1qiwlqrG6VY-017|And I add to form constructive interference between the two nuclei. |
1qiwlqrG6VY-018|And I call this a sigma bonding interaction because the electron density is along the internuclear axis. |
1qiwlqrG6VY-019|That wil be my definition of sigma orbitals. |
1qiwlqrG6VY-023|So here, I can add together px and px and get a bonding orbital. |
1qiwlqrG6VY-024|In this case, I'll call it a pi bonding orbital. |
1qiwlqrG6VY-025|Pi bonding orbitals and pi antibonding orbitals have their electron density above and below the internuclear axis. |
1qiwlqrG6VY-026|So I can get a pi bonding from the x, but I can also get a pi bonding from adding py and py. |
1qiwlqrG6VY-027|So 2 pi bonding orbitals. |
yHIDWAYbYBs-000|I have a question for you. |
yHIDWAYbYBs-009|We're talking about the reaction of hydrogen in balloons. |
yHIDWAYbYBs-011|Now, that's actually a slow step, the mixing of the hydrogen and the oxygen in the atmosphere. |
yHIDWAYbYBs-012|So this reaction will occur, and there'll be an explosion. |
yHIDWAYbYBs-013|But it'll actually be more of a [INAUDIBLE] explosion. |
yHIDWAYbYBs-014|The mixing step slows it down a bit. |
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