14.3.3: d Orbitals
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When \(l = 2\), the orbitals that are the solutions of the Hydrogen atom Schrödinger equation are called \(d\) orbitals. These orbitals only exist for shells with \(n = 3\) and greater, again because \(l\) must be less than \(n\). As we saw with the \(p\) orbitals, the probability density for the electron in space is the same for \(+m\) and \(−m\). As such, we’ll only plot the positive-\(m\) versions of the orbitals. As before, in addition to a 3d plot showing “shells” at a constant probability level, there is a 2d plot showing a cut in the \(x-z\) plane.
As with the \(p\) orbitals, as we go to the \(d\) orbitals in higher shells they get more interesting. Plotted below are the cuts through the \(x-z\) plane for the \(4d\) orbitals: