Final answer:
An electron cannot have the quantum numbers in Option D: {3, 2, -3} as the magnetic quantum number m_l is not within the required range (-l to l).
Step-by-step explanation:
The question concerns the rules for quantum numbers and which sets of quantum numbers are not allowed for an electron. To be valid, the set of quantum numbers {n, l, ml} must adhere to certain principles: the principal quantum number n must be a positive integer, the orbital angular momentum quantum number l must be an integer ranging from 0 to n - 1, and the magnetic quantum number ml must be an integer between -l and l. Using these rules, we can find out which of the options (A to E) is not a possible set of quantum numbers.
- Option A: {1, 0, 0} is valid because l is 0 (which is n-1 in this case), and ml falls within the range of -l to l.
- Option B: {3, 2, -1} is valid as l is less than n and ml is within the range of -l to l.
- Option C: {6, 1, 0} is valid because all the rules for the assignment of quantum numbers are satisfied.
- Option D: {3, 2, -3} is not valid because ml falls outside the range -l to l, as it cannot be larger in magnitude than l.
- Option E: {3, 1, -1} is valid as it also satisfies all the criteria for the quantum numbers.
Thus, the combination of quantum numbers that an electron cannot have is Option D: {3, 2, -3}.