Final answer:
The maximum number of electrons in an atom with the quantum numbers (n = 3, I = 2, ml = -2) is 2, as this specifies one particular orbital, and according to the Pauli exclusion principle, an orbital can hold a maximum of 2 electrons that differ in their spin quantum number.
Step-by-step explanation:
The maximum number of electrons in an atom that can have the quantum numbers n = 3, I = 2, ml = -2 is determined by the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers. Here, we are considering electrons with a specific set of quantum numbers, which means we are focusing on one specific orbital within an atom.
For the given quantum numbers, which describe an electron in the 3d orbital (since I = 2 corresponds to the d subshell), and considering ml = -2, we can have a maximum of 2 electrons (with ms = +1/2 and ms = -1/2). Therefore, for the quantum numbers n = 3, I = 2, ml = -2, the maximum number of electrons is 2, which corresponds to option 4).