Final answer:
A maximum of 2 electrons can have the quantum numbers n = 4, ml = -2 in an atom because this corresponds to one d-orbital, which can hold two electrons with opposite spins. The correct option is a.
Step-by-step explanation:
The student asked how many electrons can exist in a single atom with the following quantum numbers: n = 4, ml = -2.
According to the rules for quantum numbers, for any shell with n = 4, the possible values of l range from 0 to 3, corresponding to subshells s, p, d, and f. The given ml value of -2 suggests we are looking at the d subshell since ml ranges from -l to +l and only the d subshell (l=2) has ml values including -2.
Each orbital within a subshell can hold two electrons, one with spin +1/2 and one with spin -1/2 (according to the Pauli Exclusion Principle). Because we are considering the d subshell with ml = -2, there is only one such orbital. Therefore, this orbital can accommodate a maximum of two electrons, one with each spin direction.
Thus, the answer is: (a) 2 electrons.