How many electrons does gold (Au) possess that have a quantum number l = 2?
You must know that the quantum number l can take on four different values: 0, 1, 2, and 3. Furthermore, you must know that each number corresponds to a particular orbital: 0=s, 1=p, 2=d, 3=f. So the question is asking us how many d electrons gold possesses.
Since gold is in the sixth period, it has the following d orbitals: 3d, 4d, and 5d. The 3d and 4d orbitals are filled with 10 electrons each, and the 5d orbital has 10 electrons, giving a total of 30. Therefore the correct answer is C, 30.
(If you’re wondering why gold has 10 electrons in its 5d orbital instead of 9, the answer is related to the high stability of a fully-filled d subshell. From the periodic table alone, you would think that gold had 9 5d electrons, but it becomes significantly more stable if one 6s electron moves up to fill the 5d subshell. This explains why the 5d subshell holds 10 electrons!)