What ARE atomic orbitals?

what are electronic orbitals why do textbooks make them look like hard shells half the time and fluffy clouds the rest of the time why do they have weird gaps in them and where can we see things like orbitals in the world around us keep watching to find out now before we start I need to say that electronic orbitals are fundamental concepts in quantum mechanics and that means that there are simply no accurate and correct qualitative explanations of what they are so I can show you equations and graphs but as soon as we try and explain what they mean we have to decide how inaccurate they're going to be and the more correct those explanations are the more inaccurate they are going to be and the more accurate those explanations are the less understandable they are going to become to anybody so for now I'm just going to say that an orbital is a space where we are likely to find an electron and that space has the shape of an oscillation which is pinned to the nucleus at the center of an atom and if you wanted deeper explanation of why that is make sure you hang around for the bonus extras at the end of this video so how can we understand what we mean by an oscillation where we are likely to find something well I've got a couple of demonstrations for you so let's take a look the first point I'm going to tackle is the orbitals only exist when there is an electron in them so how can a space with a shape suddenly appear when an electron arrives well let's start by having a look at this Plaza there's a kind of orbital for humans down there and it's a big one can you see it no well that's because it doesn't exist without humans so let's put some in now what I'm doing here is stacking up photographs taken over a period of time the human particles appear as slightly invisible ghosts so places where we are more likely to find a human at any given time are darker than other places in other words we are creating a density plot of humans and now you can see a kind of shape there there are no roads or fences keeping people to that shape but I knew it would be there why because there are entrances to two big buildings at either end of that Plaza and people will tend to follow the lowest energy path between those two entrances and that means that even though the square is mostly open and humans are free to go anywhere that they want they are most likely to be following those low density paths and that makes this shape in our density plot and of course we can find them in other places it just means they will have to take more energy to go to those areas and we will be less likely to find them there and if we divide the photograph up into lots of tiny squares we can use the darkness of each Square to calculate a probability of finding a human there and then we can plot a map of human density and it's much easier to see that shape if we choose a minimum probability let's say 10 and just color it in nice and solid but remember a more accurate depiction is a fuzzy cloud and you can also imagine that if it was just one person but we took the photographs over a longer time say a few years we would end up with the same kind of density plot so this is our first example of something that is like an orbital we just take a bunch of pictures over a long period of time squash them all together in other words we're taking time out of our simulation and we get a space that spontaneously appears when there are particles in it because that space only appears as a result of those particles interacting with their environment now the next demonstration is even better but I forget if you could just click the like button that'll help us make more videos thanks now for our next demonstration we're going to take a trip to the Fukuoka City Science Museum you see I was there one day when I saw something that I really wanted to show you so Mr hisao Tanaka one of the senior demonstrators at the science museum kindly allowed me to film it for you and here it is it's a plastic tube with some polystyrene balls at the bottom not impressed how about now [Music] so what's going on well there's a speaker at one end of the tube and it's closed off at the other end of the tube so if and only if the wavelength fits perfectly into the tube we get a standing wave so what's this got to do with electronic orbitals well we can also use a wave function in this case a simple sine function to model the sound wave in this tube and then we can use that same wave function to calculate the probabilities of finding polystyrene beads at certain places along the tube in other words if we find the nodes according to our wave function then we are likely to find polystyrene beads there too and that's similar to an electronic orbital an orbital doesn't tell us exactly where an electron is it's not a kind of solid container for for electrons but rather other it tells us where an electron is most likely to be now we could say that fractional waves don't fit but it's more accurate to say that fractional wavelengths bounce up and down the tube and interfere with themselves to cancel themselves out and they just don't get that stable pattern also in the tube we can talk about a polystyrene B density and we could do that by taking just a few pictures of lots of beads or we could do it by taking a lot of pictures of just one bead moving around well we could but actually that didn't work and it didn't work because the single bead is moving along the bottom of the tube and that means friction stops it from fitting nicely into the nodes but you can imagine how it would work so in a similar way we can talk about electron density we might be talking about many electrons in a large space or just one electron in a small space and understanding electron density is a big part of chemistry and we can even get an idea about energy levels you see the beads are attracted to the bottom of the tube by gravity so that means the higher up they are the more gravitational potential energy they have now two beads can't be in the same place so we can sort of see discrete energy levels and if a bead has a space underneath it it'll drop down and lose its energy and then it won't be able to get back up again and that's just like electrons losing their energy and falling down to a lower energy level and getting stuck there until they get some extra energy from somewhere else and we can even see similar Behavior with grains of sand with two-dimensional waves there's lots of videos on YouTube so I'll drop a couple of links in the description and you can check them out now one of the big differences between this demonstration and electronic orbitals of course is that the sound tube is effectively one-dimensional whereas electronic orbitals are three-dimensional and centered on a tiny point the nucleus but in three dimensions waves don't just have a frequency they have a shape and there are only certain waves that we can attach to the tiny point of a nucleus so that is why we find electrons in these strain shapes centered at the atom and as we get further away from that nucleus we find that the electrons in those orbitals have more potential energy just like the beads at the top of the wave so we've had one-dimensional waves I've linked to two-dimensional waves and the obvious Next Step was to go with three-dimensional waves and I spend quite a lot of time thinking about how to do that and then I realize that there actually wasn't much point because this analogy is exactly wrong and that's because the beads here are where the waves aren't they're in the nodes but in the Schrodinger equation the electrons are where the waves are it's exactly opposite so a better way to visualize the Schrodinger equation with this demonstration is to take the negative of the video and now we can see where the waves are in a way that corresponds to the wave function of this Schrodinger equation now there is a minority branch of physics called bomia mechanics which treats electrons as if they are particles being carried on a wave I've put a link in the description if you're interested but it does seem that most physicists are convinced it's incorrect so let's put these two demonstrations together and see what we get we've seen that taking a chunk of time and squashing it together can show us a space where we have a high probability of finding a particle and we've also seen that we can use the mathematics of a wave a wave function to predict the probability of finding a particle at a certain point in space even though that wave function doesn't tell us anything about how the particle actually moves the Schrodinger equation combines these two things the wave function gives us the shape of the orbital and the hamiltonian operator relates that wave function to particle densities so let's take the simplest possible atom hydrogen the wave function in the Schrodinger equation is the function of a stable wave pinned to that tiny nucleus at the center of the atom now the simpler shape for doing that is a sphere and as we increase the frequency or the energy that oscillation will self-interfere and cancel itself out until we double the frequency and at this point we have a shell-like gap with almost no probability of finding electrons and this is a node just like the nodes that we saw in the sound tube and as we continue increasing that frequency the nodes become more significant and the sphere breaks into two halves with each half having a different phase I'm going to talk about phases in more detail for a different video but for now you should already know about one-dimensional waves and phases how one part of the wave put goes up and the other part of the wave goes down and those crests and waves can interfere constructively and increase their amplitude or interfere destructively and cancel themselves out and that'll be important to remember if you want to understand how atoms can come together merge their orbitals and make molecules now let's talk briefly about the energy of orbitals because electrons are attracted to the nucleus the more we pull them away from the nucleus the more potential energy they have and that's just like the polystyrene beads in the sound tube as they were moved higher and higher in the sand tube they were pulled away from their attraction to the ground and they had more and more potential energy but because the oscillations that the electrons are sitting in are so much bigger than the nucleus the electrons have to spend most of their time away from the nucleus and the bigger the orbital is the more time on average the electrons will be sitting even further away so the larger the orbital the more potential energy that electron must have in addition the more nodes that an orbital has the higher its energy and there are a couple of ways of thinking about this first of all waves with more nodes are higher in energy than equivalent waves with fewer nodes but we could also imagine that an electron trying to follow a certain space needs more energy to follow a squiggly path than a simple circular path a really important point to take away here though is that it's not the orbital that has the energy it's the electron sitting in the orbital and yes I also say this is a high energy orbital but that's because it's so much easier to say this is a high energy orbital than it is to say the electron sitting in this orbital has a high potential energy now I haven't explained why you can only get two electrons in an orbital and I'm not going to because there are no good qualitative explanations for it yes it's supposed to be about spin and yes you have to have gears that move in opposite directions to pair them together but number one electrons aren't spinning and number two you can connect as many gears in a line as you like so for now we're going to just be happy with the idea that you can only have two electrons in an orbital and they have to have opposite spins all right let's recap where we've got so far number one we've seen that by stacking up images to squash down time we can reveal a shape in space that only appears by the interaction of a particle with its environment number two we've seen that we can use the mathematics of a wave to predict where we are likely to find a particle and three we can understand how orbitals with different sizes and different shapes can be associated with different potential energies so what can we do with all that well we can imagine taking photographs of an electron as it moves around in its orbital and then we can imagine taking those photographs stacking them up and squishing time together just like we did for the photographs of people in the plaza now what we're really doing is is calculating the probability of finding an electron around a nucleus using the Schrodinger equation so where the oscillation vibrates the most is where we are most likely to find the electron and then we distribute 300 points around our imaginary nucleus according to those probabilities and this is what we get you can see that we get a cloud effect there's no solid container the orbital itself doesn't have energy it's just a space where we are likely to find an electron but the average potential energy of that electron depends on which orbital it is occupying so finally we can understand that diagrams like this show us that cloud nature just with many more points and we can also see that if we set a minimum probability of finding an electron let's say 95 percent we can draw a hard shell around that space and that hard shell makes it easier for us to see the three-dimensional shape of the orbital even though it might confuse us and make us think it's something solid so there you go an orbital is a space where we are most likely to find an electron it has the shape of a three-dimensional oscillation and centered on the nucleus and it's not the orbital itself that has the energy it's the electron sitting in that orbital that has the energy okay let's take a closer look at quantum mechanics in our everyday macro scale World particles and waves are completely different things we can take a little ball and we can say exactly where it is it's there and we can see where it's moving it's going that way but waves are completely different if I make a wave right now where is it um where is it going well we can't really talk about waves in that way where is it well it's all around the room and in fact some of it is outside the room and if we had a super sensitive microphone we could be on the other side of the street and still detect the wave out there so it's very difficult to say exactly where a wave is and where's it going well it's kind of going backwards and forwards and it's over there and over here anyway so maybe it's not going anywhere but still things are moving so the words that we use for particles do not work with the way that we talk about a standing wave and vice versa but on the scale of atoms and Below we can't make that distinction anymore sure we can pin an electron into one place but then we don't know where it's going we fundamentally cannot talk about that the same way that we can't talk about which way is a standing wave going and we can also get our electrons to behave like waves we can get them to diffract and spread out but then they arrive at a detector as a single point which is something that waves cannot do in other words at that scale we can no longer talk about particles and waves as being separate things rather we have to say that our particles have a wave nature and a particle nature combined and that's why there are no good qualitative explanations for quantum mechanics because there is nothing in our macro scale world that behaves like that sure we can make our explanations more understandable but the more we do that the less accurate they are and if we go the other way to make them more accurate then the less understandable they are to anybody so our final more accurate explanation of what an orbital is is that it's the wave nature of an electron oscillating around a nucleus and the density plot is the particle nature of an electron flashing into existence for an instant without any way of knowing where it's going to show up next in other words the orbital and the electron are two aspects of the same thing and if that doesn't make any sense to you right now don't worry physicists are still arguing about what it really means so what do you think do you have a better way to explain orbitals would you like to hear about how orbitals come together to extend over a whole molecule or throughout a whole Crystal are there any other Concepts you'd like to hear about from chemistry let us know down there in the comments and I'll see you next time

Channel: Three Twentysix

Views: 263,049

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Id: 23bNW4G9DZk

Length: 21min 34sec (1294 seconds)

Published: Sat Aug 12 2023