We've looked at Bohr's model of the atom, and Bohr's model had some limitations. So we're going to in this learning objective be able to extend our understanding of the electronic structure from Bohr's model to what's called the quantum mechanical model. So let's look at what's called the uncertainty principle. We do know that electrons have a wave nature. Because, if the electrons come at two slits, they behave as partic-, they would behave as waves. We see this diffraction pattern over here. We also know that they have particles, they have mass. Okay. We can detect those particles as well. So we see the wave nature. We see the particle nature. We know that they have a dual nature. The amazing thing about this is you cannot de, design an experiment where you observe both simultaneously. Now if you had a laser, and that's what this is representing here, if you have a laser and you pass electrons through it, you'll see it as a particle, because it will flash. You'll see it flash and cause the laser beam to have this, this flashing occur. So if you were to put that laser beam in front of the, the slits. The expectation was, all we can see the dual nature. We can see them flash up as they pass through and then we should see them behave as a wave. But as soon as we see that flashing and see that nature of those electrons as particles we no longer see that defraction pattern. Instead we just see it lighting up in the two places across from the slit. So we only see that particle nature at that point. So if we try to observe both aspects, the wave nature and the particle nature simultaneously, we always fail. There is a principle called the Heisenberg uncertainty principle and here's the mathematical expression of it. So let's define the pieces. We've seen Planck's constant. We certainly know what pi is. But delta x is the uncertainty in the position of the electron. Okay? So the more accurately you know the position of the electron, the more you narrow in on where it is located, the smaller this delta x would be. The uncertainty in the velocity is the delta nu. And the more certain you know how much velocity that electron has, the smaller this term is going to be, okay? So we have these two pieces and they're in here, okay. Because of this greater than symbol here, greater than or equal to, we know that this term has gotta stay bigger than, it can't get smaller than this fraction on this side. What does that tell us? Well, this tells us the more accurately, we know the position. So, the smaller this term gets, okay. The bigger this term is going to have to get in order keep the left hand side larger than the right hand side. And of course conversely we would be able to say that the more accurately we know the velocity, so the smaller this term is, the larger this term is. Because we have to keep that product larger than what's on the right hand side. So this gives us a complication. Now if we forget about electrons for a minute and we talk about trains, the old mathematical problems of a train leaves a station at this time traveling at this speed, and you ask at what time will it arrive at the next destination, you know that train, where it is and its velocity. So you can, with certainty know where it's going to be at any point. We don't have that with the electron. We can say, well maybe it's traveling at this speed, but we don't know where it is. Or we can say we know where it is, but we don't know how fast it's traveling. This gives us a lot of complications with our electron. And leads us to the mathematics that leads to the quantum mechanics of the atom. So instead of thinking about the electrons moving as orbits, so they're not traveling around in orbits like planets around the sun. If they did that, we would know, okay, this is where it is right now. This is how fast it's traveling, we can predict where it's going to be at any point down the road. We don't have these orbits. Instead, what we have is defined regions in space where we have a high probability of finding the electron. So we can, we can kind of zero in into an area, but we can't go into a precise orbit. Okay, so Schrodinger developed mathematical equations that are used to define these regions in space. The Schrodinger equations are quite complex. They take into the account the particle nature of the electron. They take into account the wave nature of the electron, and they require a lot of calculus to define these regions in space. But these give us areas where there's a high probability of finding the electron, and we would say it has a high electron density. So I already told you that, they take into account the dual nature of the electron. And this is watch, what launched, what was called, what we call quantum mechanics. Now, if you're in, going to be taking chemistry as a major, you will get into deriving these equations. And you will look very much into the mathematics of these equations. For general chemistry, we will not, not do that. We will look at the outcome of those equations. So, those equations define these areas in space where you have a high probability of finding electrons. And we call these regions orbitals. So we've lost the word orbit but they've tagged kind of on that idea and they're called orbitals. Okay, so that's the end of that, just introducing to you the fact that we're moving away from the idea of orbits. We're moving into this idea of orbitals, regions in space, where we have a high probability of finding electrons. And what we'll do next is examine these Schrodinger equations, actually we won't look at the mathematical equations. We'll look at the outcome of those equations and see what they tell us about the orbitals of the atom.