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Why do the suborbitals for d start at 3 instead of four? It is in the fourth row on the periodic table and all other suborbitals start according to the row on which they are located except for d. Why is that?

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This is due to the underlying quantum physics. Quantum physics teaches us that orbitals are ultimately a result of so called quantum numbers that appear during the mathematical description of these quantum mechanic systems.

If you do the math you'll see that in the 3rd period there's the main quantum number $n=3$ which allows the secondary quantum number $l$ to take the values 0, 1 or 2. As $l$ determines the kind of the orbital you get a $s$, $p$ or $d$ orbital.

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