Final answer:
The set of quantum numbers {n = 4, l = 3, m = 0} is not allowed because l is greater than n. The other sets of quantum numbers are allowed.
Step-by-step explanation:
The set of quantum numbers {n = 4, l = 3, m = 0} is not allowed. The principal quantum number (n) represents the energy level of the electron, and it cannot be negative or zero. The azimuthal quantum number (l) represents the shape of the orbital and it must be less than n. The magnetic quantum number (m) represents the orientation of the orbital and it must be between -l and +l inclusive. In this case, l is greater than n, which is not allowed.
All the other sets of quantum numbers are allowed. In option B (n = 2, l = 2, m = 2), the values of n, l, and m meet the restrictions. In option C (n = 3, l = 3, m = 3), the values of n and l meet the restrictions, but m must be between -l and +l inclusive, so this set is not allowed. In option D (n = 1, l = 1, m = 0), the values of n, l, and m meet the restrictions, and therefore this set is allowed.