Final answer:
Among the options provided, choice (B) {2, 1, 0, -1/2} is a valid set of quantum numbers for an electron in an atom, as it adheres to the rules governing quantum numbers. Options (A) and (D) are also valid, while option (C) is not because it violates the rule for the azimuthal quantum number.
Step-by-step explanation:
The quantum numbers of an electron in an atom describe its state and must obey certain rules. These quantum numbers are principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m), and spin quantum number (ms).
Among the options provided, choice (B) {2, 1, 0, -1/2} is a valid set of quantum numbers. This is because it follows the rules: n can be any positive integer, l can be any integer from 0 to n-1, m can be an integer from -l to l, and ms can be either +1/2 or -1/2. Option (A) {1, 0, 0, 1/2} is also valid, as its numbers fit within these constraints. However, option (C) is not allowed because l is equal to n, which breaks the rule that l must be less than n. Finally, option (D) {4, 2, 2, -1/2} is valid following all the rules.
According to the Pauli exclusion principle, no two electrons in the same atom can have exactly the same set of these four quantum numbers, which explains why electrons in the same orbital must have opposite spins.