How many d orbitals exist for energy levels n=3 and higher?
Answer
Five
The various shapes that atomic orbitals can assume are categorized by letters corresponding to the angular momentum quantum number, $l$. The $d$ orbitals correspond to $l=2$. For any given principal energy level ($n$) that is high enough to contain them (which starts at $n=3$), there are always a specific number of orientations available, dictated by the possible values of the magnetic quantum number. Specifically, there are five distinct $d$ orbitals ($m_l = -2, -1, 0, 1, 2$). These five orbitals typically manifest as more complex shapes, often described visually as four-leaf clovers, allowing for the nuanced interactions seen in transition metal chemistry.
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