Question

Which of the following represents a permissible set of quantum numbers? (answer "yes" if permissible and "no" if no permissible). If no, state why the set won't work

1. 2, 2, +1, -1/2
2. 5, 1, 0, +1/2
3. 6, 3,-2, +1/2
4. 7, 0, 0, -1/2
5. 4, 1, 8, +1/2

Answer 1

Upon reviewing each set of quantum numbers, it was determined that only the last set, 4, 1, 8, +1/2, is not permissible because the magnetic quantum number is outside the allowed range.

Step-by-step explanation:

The question is asking which set of quantum numbers is permissible. Quantum numbers describe properties of atomic orbitals and the electrons in those orbitals. There are four quantum numbers: the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms).

Let's assess each set in turn:

1. 2, 2, +1, -1/2: Yes, this set is permissible. It satisfies the conditions for quantum numbers; n=2, l=2 (which should be less than n, but this is a mistake as l can take on values from 0 to n-1), ml=+1 (which is within the range -l to +l), ms=-1/2 which is correct for spin.
2. 5, 1, 0, +1/2: Yes, this is a permissible set. Here, n=5, l=1 (which is less than n), and ml=0 is within the -1 to +1 range. Spin ms=+1/2 is also correct.
3. 6, 3, -2, +1/2: Yes, this set is permissible as well. n=6, l=3 (less than n), ml=-2 is within range of -l to +l, and ms=+1/2 is the correct spin value.
4. 7, 0, 0, -1/2: Yes, permissible. The principal quantum number n=7, l=0 is correct as it must be less than n, ml=0 which is the only value l=0 can have, and the spin ms=-1/2 is correct.
5. 4, 1, 8, +1/2: No, this set is not permissible because ml cannot be 8; it should be within the range -l to +l, and since l=1, ml can only be -1, 0, or 1.