This section deals with the basics of quantum mechanics. Don’t worry too much about it, but this is some good general information.
Definition of an Atomic Orbital:
These funny orbital shapes represent the 3-D plots of the equations that describe the probability of finding electrons at any given place as their energy states increase.
The probability of finding electrons in a given place.
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Why is quantum mechanics important? Why we have to talk about it for or go? Because maybe you guys remember that the smaller particles get, the more that they're going to function as both particles and as waves. Okay, so what that means is that in regular physics, if you have a ball in it hit something and it collides. That's we call Newtonian physics, right. But as these particles get very, very small, for example, electrons they're not just gonna behave as particles anymore. They're not just gonna have collisions. They're also going to behave as waves and interfere with each other with each other. Okay, so there are these mathematical equations that make this the math is very confusing. We don't need to know all that, but we do need to know a few things. For example, the Heisenberg uncertainty principle. What does that mean? Well, what that says is that because these are acting as waves, we can't simultaneously no, an electron speed and its position. Okay, we can no one or the other. We could know where it is and but not how fast it's going. Or we could know how fast it's going, but not where it is. Okay. What that means is that instead of focusing so much on where the electron is at a given moment, what we're gonna do is we're gonna focus more improbabilities. We're gonna say, OK, what are the chances that an electron is in this space? Okay, And that's actually gonna be a lot more important for this course. So remember that I was just talking about these mathematical equations. Well, the reason that these equations air complicated is because these aren't just particles these air acting as waves, it z there's a lot more complexity to it. And the way that we describe these is through wave functions. Okay, so you can think of a function in math, right? It's just an equation that's going to describe the energy state oven, electronic given time, all right. And there is a Greek letter that we used to symbolize the wave function. So go ahead and circle that. It's the Greek letter sigh. Okay, so I kind of drew a bad sigh, but whatever, that's a sigh. OK, The Cy is my letter to substitute for this way function that I'm not gonna teach you because it would be way too long and way too tedious. Alright. But it turns out that if I derive if I take a derivation of that equation and in fact, if I square it so the size squared, What that's going to give me is the relative probability off finding an electron in a certain space. Okay, so that's really important. Because now, if I could take that equation and square it, that's gonna tell me what are the chances that electron is in a certain place? And that's what's important to me as an organic chemist. Alright, so finally, where does this all go? Finally, if you take the three d plot of this size square because, remember, this is just an equation. Okay, So if I take a three d representation of it and so just right here of the size square, what I'm going to get is a region of space called in atomic orbital. Alright, so that's where this all comes together. Basically using these really fancy equations to describe where are electrons gonna be okay? And that is what we call the atomic orbital. So the atomic orbital is just a mathematical representation of where these electrons might be at a given time. And that's a That's a place where the chances of finding electron are high. So now let's go ahead and talk a little bit about what the's orbital's look like. All right, I know you guys might remember this from Gen. Campbell. Let's go over it really quick. The simplest type of orbital is the one s orbital. The one s orbital is just a sphere. It's kind of small. That's it. Okay. Remember that the first shell can hold two electrons and the one s orbital. Each orbital hold how many electrons to? So that's it. There's really nothing more to know. That first shell only has one orbital on one s. Okay, then, once we get into the second shell, the second shell we're gonna learn can actually hold eight electrons, Okay? And I'll just put these okay, eight electrons. And what that means is that it consists of four different orbital's that can hold two electrons each. The first one and the lower energy one is gonna be the two s. Now, the two s looks a lot like the one s. It's just bigger because these electrons, and are a little bit further away from the nucleus. So they have a little bit more energy. Alright, so that one can also help to hold to. And then finally, we have these three orbital's, um that are a little higher energy state, and they're all the p orbital's. And the way that I think of it is that they kind of look like peanuts. Okay, you're you're Professor might have said dumbbells or whatever. Whatever the case is, I just think that they look like peanuts. So there's three of these. They go in different directions. The important part to know is that they all have the same energy and they can hold two electrons. Good. So what if we were, for example, trying to draw the atomic orbital diagram for carbon? Let's say we're doing carbon right here and try to figure out where the electrons are going to go. So first of all, you guys have to tell me how many electrons would a carbon atom have? You would have six. So let's go ahead and write six electrons, okay? And that's because carbon has an atomic number of six, so it would have the same amount of electrons so Where do we put these electrons? Well, the first two should definitely go in the oneness. Okay, so now I have my two first electrons with lowest energy state possible. Now that energy status full, that shell is full. So I have to jump up to the next higher energy. And that would actually be the two s. Remember that I said to us is a little bit more. I would then put two more electrons into two s. Now, I have four electrons that are filled in orbital's, but I still have two left. Where do you think I should put those? This is a little trickier. I should put them in one of the Pete. I should put 11 p orbital and one in another p orbital. Okay, now, just so you know, all three of these p orbital's are mathematically equivalent, but it's just normal convention to use x and Y first. But if you wanted Thio, if you really wanted to be a rebel, you could use the first. But it's just your professor would just think like what are you doing? Right? So also noticed that I drew them with an up spin. If you drew them with a down spin. That would also be fine. As long as you're consistent. Don't draw one up and one down. That would be bad. But if you draw them both down, that's fine. Alright, cool. Just you know, this little meme that I drew, I actually I made this because it's like a short, short enders cat is a thought experiment to talk about that a cat could be half alive or half dead at the same time. It's used to talk about how electrons could be in one place where they could not be in one place. So it's interesting whatever this this mean did not go viral. So I should probably just stick to organic chemistry, right? Because it wasn't I guess it wasn't that funny.
Atomic Orbital Interference
Instead of colliding into each other, wave functions have the ability to interfere with each other upon meeting.
The type of interference determines if a new bond will be created between the two orbitals.
Constructive vs. destructive interference.
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Hey everyone. So in this video we're gonna take a look at wave functions. But before we get to them, let's talk about the importance of quantum mechanics. So why is exactly quantum mechanics and important topic? Well we need to understand is the smaller an object gets, the more likely it can behave as either a particle or a wave. And this comes with great complications in terms of determining the location of that particle, how it's moving etcetera. Now, quantum mechanics is what states that electrons because they're so small, behave both as particles and as waves. And with quantum mechanics we have the Heisenberg uncertainty principle which states that we cannot simultaneously know an electron speed and position. So we might know the speed in which an electron is traveling but we won't know its position or we may know its position but not know how fast it's moving. So because of this issue we more focused on the probability on an electron's location. And this is where wave functions come in handy. So we're gonna say equations called wave functions correspond to the energy state of an electron. And to symbolize this wave function, we use the symbol of sai okay, so wave functions is corresponded by this image of a sigh and we're gonna say the relative probability of finding an electron can be derived from the way function. And we do this by squaring our side. Okay, so here again we don't know both the speed and position of an electron. So we're talking about the probability of finding an electron location instead. Now we're going to say here that the three D plot of the y squared. So relative probability is called an atomic orbital. So coming from general chemistry, we know that an orbital is the probable location of any defined electron. So this is our chance of finding electrons. Words where it's going to be high. Now, remember from general chemistry we talked about different types of orbital's. So we have s orbital's which are spherical in nature like one S and two S. And then we have p orbital's which look like dumbbells. But an easy way to remember the shape of a p orbital soapy here. Peanut also starts with a P these kind of look like peanuts. Okay, so that's a good way to help you remember the shape of a p orbital. Now, remember when we talk about these different orbital's, they're found within different energy levels. So we're looking at let's say the carbon atom, we can talk about how can we display its orbital diagram remember for carbon, Its atomic number is six, which means it has six electrons. So that means its electron configuration is one S 22 us two to P two. Now let's start filling out each one of these orbital's first of all, remember an S orbital has only one orbital, its shape is spherical in nature. Remember that each one of these orbital these boxes can house a max of two electrons. And following what we call the exclusion principle, we're not gonna go too much into those things. These are simple things that we learned in jen can remember the electrons in there have to be have opposite spins. So we have one electron spinning up and then we have one electron spinning down. Now the order doesn't really matter which one you write first, they just have to have opposite spins. Once we filled up the one s we move on to to us us has more energy and we moved from lower energy orbital to higher energy orbital's following off balls principle. So here we go, one up, one down now the two P. S. There's three of them, there's X, Y and Z. Okay, they all have the same energy since they're all two p orbital's the only difference is is the position in which they lie on the X axis, the y axis and Z axis, but they're all the same energy because of this, you could technically start filling them up at PZ if you want. But traditionally we fill them out, starting with P X. And we're going to say here following our half half spin roll. So Hunt's role we have felt first we have to fill in two electrons. So one up one up, you could also do one down, one down. That would also work as well. But traditionally start out with the one spinning up first. Now if we look at this, this is how we complete the orbital diagram for the carbon atom. So this tells us that in the first show which only houses the one s orbital, we have a maximum of two electrons possible and in the second show we have both two S and two p orbital's. This in theory can hold up to eight electrons. It doesn't hold it for carbon because carbon just doesn't have enough electrons. It only has four total electrons within our second show. And then here we have our little meme. In terms of remember we had schrodinger's cat. Remember with shorting just cat it was the possibility of being both alive and dead. So quantum mechanics states that I am simultaneously half alive, half dead. So this kind of goes in relationship to electrons where the electron could be in this position or it might not be. So there's a half chance of being there or not. So this kind of like goes hand in hand with that concept. So, just remember, we can't know both the speed and position of an electron, but we can talk about the probability the most likely location of an electron and that most likely location of electron can be defined as orbital's