Consider the following sets of quantum numbers (n, l, m, s):
(i) 3, 0, 0, +1/2
(ii) 2, 2, 1, +1/2
(iii) 4, 3,

Question

Consider the following sets of quantum numbers (n, l, m, s):
(i) 3, 0, 0, +1/2
(ii) 2, 2, 1, +1/2
(iii) 4, 3, -2, -1/2
(iv) 1, 0, -1, -1/2
(v) 3, 2, 3, +1/2

Which of the following sets of quantum numbers is not possible?

Accepted Answer

We apply the selection rules for quantum numbers to determine validity:
1.  **Principal Quantum Number (n):** Integer > 0.
2.  **Azimuthal Quantum Number (l):** Integer where $0 \le l < n$.
3.  **Magnetic Quantum Number (m):** Integer where $-l \le m \le +l$.

**Evaluation of Sets:**
*   **(i) 3, 0, 0, +1/2:** Valid ($l=0 < 3$, $m=0$). Corresponds to 3s.
*   **(ii) 2, 2, 1, +1/2:** **Invalid.** $l$ cannot equal $n$ (max $l$ for $n=2$ is 1).
*   **(iii) 4, 3, -2, -1/2:** Valid ($l=3 < 4$, $|-2| \le 3$). Corresponds to 4f.
*   **(iv) 1, 0, -1, -1/2:** **Invalid.** If $l=0$, $m$ must be 0. $m=-1$ is not allowed.
*   **(v) 3, 2, 3, +1/2:** **Invalid.** If $l=2$, max $m$ is +2. $m=3$ is not allowed.

Therefore, sets **ii, iv, and v** are not possible.

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