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The way this can be calculated is that d-orbitals exist in n=3 or above, which means that l=2 (so there are s, p, and d orbitals). When l equals 2, ml can equal -2, -1, 0, 1, or 2 (5 orbitals). In each of these orbitals there can be a maximum of 2 electrons, where one of the electrons has an up spin and the other has a downward spin ( a spin pair). So, if you have 5 orbitals where each orbital can have 2 electrons, you get 2*5= 10 electrons
Since d-orbitals have 5 orbitals, they can hold 10 electrons as each orbital can have a spin up and spin down pair. This means that, with the d-orbital in play, there can be up to 18 valence electrons as s-orbitals can have 2 electrons and p-orbitals can have 6 electrons.
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