 So what we'll do in this video is illustrate some more drawn to scale pictures of what these wave functions look like. So the pictures you see on the side here are actual mathematical representations of the probability of finding electrons around that orbital. So each one is labeled with their quantum numbers. 200 is the 200 wave function, of course, but we've learned that the more common name for that wave function is the 2s orbital. So what we've seen is in the 2s orbital there's a radial node and you can see that radial node which I'm unable to draw in a way that's not obscured by the wave function but you can see the radial node is the place the dark region where the electron is not found at all and likewise if we move up to a larger value of n to the 3s orbital then the 3s orbital has two angular nodes, two radial nodes, sorry, one at a smaller distance and one at a larger distance. So you can see the inner and the outer radial nodes of this wave function. When we move up to larger angular momentum quantum numbers, so when l equals 1 then we get p-type orbitals. So this is the 2p orbital, in particular the 2pz orbital, the one that's oriented along the z-axis and now rather than having a radial node we have an angular node so this flat region right here which we can draw as the plane containing the x and y-axis that's an angular node because at that particular value of theta, theta equals pi over 2, we're never going to observe the electron. And then the 2p, the 2-1-1 orbital is just a different orientation of one of these p orbitals. The 3p orbital shown here for the 3-1-0 wave function again has both a radial node, the sphere right here that where we never find the electron as well as the x-y plane so we have both an angular node in the x-y plane where the theta equals pi over 2 plane as well as a radial node at this particular value of r where we never find the wave function. So we won't illustrate all the rest of these but as we move higher to d orbitals for example with the l value of 2 or even to f orbitals with an l value of 3, we get more and more angular nodes. When we move to higher n values like this 4p orbital here, we collect more and more radial nodes. So just to summarize the properties of these different quantum numbers and how they affect the shapes of these orbitals and their size, one thing that the n quantum number tells us is the size of the wave function. So as you can see the 3s wave function is a little bit larger than the 2s wave function which is not a surprise. Atoms get larger as they move down the rows of the periodic table because they occupy larger principal quantum number orbitals. L, the quantum number, so the main difference between let's say an s orbital and the p orbital is not the size of the orbital but the shape of the orbital. So what l is really telling us is the angular momentum of the orbital and what that means in a quantum mechanical sense if an orbital has no angular momentum it behaves in this spherical manner it occupies a spherical orbital. If an electron has a little bit more angular momentum meaning it's oscillating a little bit in theta then as it oscillates from positive to zero to negative in the wave function then that introduces a node. In a d orbital it oscillates from positive to zero to negative to zero more often as it goes around each value of theta. So the larger the value of l the larger the wave function the more the wave function is oscillating in theta and the more angular nodes they get introduced. So what angular momentum practically means is that that has an effect on the shape of the wave function. The l value tells us a lot about the shape largely whether it's an s orbital or a p orbital or a d orbital or an f orbital and so on. The m quantum number, the magnetic quantum number on the other hand is telling us for example the 2p z orbital and the 2 1 1 orbital those differ primarily in the orientation of those two orbitals. Likewise the 2p x 2p y 2p z orbitals differ primarily in the in the direction in which they point. So m is telling us the orientation l the shape of the orbital and the relative size of the orbital. The next thing that's important to understand if we want to sketch an arbitrary orbital is we need to understand how many nodes to draw and we can use either the mathematical equations for the wave functions or this chart as a reference and can convince ourselves relatively easily that the number of radial nodes has something to do with n. As we go from n equals 2 to n equals 3 we always introduce one extra radial node but it's not guaranteed that we'll have one radial node every time n equals 2 for 2p orbital we only have an angular node and not a radial node. So it turns out that the number of radial nodes increases when n increases but it decreases when l increases. So the number of radial nodes is n minus l minus 1 for example for this 2 0 0 wave function 2 minus 0 minus 1 gives me the one radial node that the 2s orbital has. And if we want to determine the number of angular nodes that's a little bit easier that's just the value of l. So an s orbital where l equals 0 doesn't have any angular nodes. A p orbital like these two where l equals 1 has always one angular node. A d orbital like this one or this one has two angular nodes. You can see one here and one here. This one also has two angular nodes but because of the point of view one is the plane sticking out of the board this way the other is in the plane of the board slicing the molecule in half front and back but you can't see it because the angle you're looking at this wave function from. So this would be like a dxy orbital. So that tells us the general shape of the orbitals determined by l, their size and their orientation and we can know how many angular and radial nodes to divide those wave functions into if we also know the values of n and of l.