Final answer:
The maximum number of electrons with the specific quantum numbers n = 4, ℓ = 3, mℓ = 3, ms = -½ is one, due to the Pauli exclusion principle that prohibits two electrons from sharing the same set of quantum numbers.
Step-by-step explanation:
The question pertains to an application of the Pauli exclusion principle, which in quantum mechanics, states that no two electrons can have the same set of four quantum numbers. Given the quantum numbers n = 4, ℓ = 3, mℓ = 3, ms = -½, we can determine the maximum number of electrons that can occupy this state.
For any given set of n, ℓ, and mℓ, there can be a maximum of two electrons, differing only in their spin quantum number ms. However, since we are given that ms = -½, there can be only one electron with this specific set of quantum numbers. If ms were instead +½, that would account for the second possible electron.
Therefore, for the given quantum numbers, the maximum number of electrons that can be present is one.