Here we will investigate the shapes of the different orbitals. Remember that an orbital is a region where electrons are more likely to be found. Also remember that in each orbital, there can be up to two electrons and no more.
Before you look at the following diagrams, keep in mind that where the x, y, and z axes intersect, or the origin, is the nucleus. Also, the volumes of the electron orbitals are very huge compared to the volume of the nucleus.
Lets look at the first figure, which is the s orbital. The density of the dots represent the probability that one would expect to find the one or both electrons that the atom has in that orbital. For example, notice the orbital is very dense near the center and becomes more sparse as the distance from the nucleus increases. This means that one would be more likely to find the electron or electrons near the center. Why? Because electrons tend to have a lower energy state; as their distance from the nucleus increases, so does their energy.
The image to the left resembles a sphere at the origin; however, it is the exact same orbital as the image above. The surface is the "outermost point" that an electron can go. For all subsequent images, we will illustrate orbitals as a solid rather than a probability chart.
Now lets look at the different p orbitals. Remember that there are three p orbitals in every sublevel except the first. Look at the following figures.
Finally, let's look at the d orbitals. Remember that there must be five different d orbitals in every sublevel except the first and the second.
In the first figure, the four lobes lie across the xz plane and this orbital is called the dxz orbital. It is easy to be misled by the implication that there must be four electrons for each d orbital, since there are four lobes. However, remember that there are only two electrons possible for each orbital. Look at the last figure; the lobes lie across the yz plane and the orbital is the dyz orbital. Likewise, the first figure illustrates the dxz orbital. The third figure is the dx²-y² orbital and the second figure is the dz² orbital. Although the dz² orbital does not look similar to any of the other four orbitals, they all have the same amount of energy. The figure below illustrates how all the orbitals combined together would appear in the atom.
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