Quantum Numbers

Mediumchemistry

Which set of quantum numbers (n, l, m_l, m_s) is NOT allowed?

Select the correct option:

(3, 2, -2, +1/2)

(2, 1, 0, -1/2)

(4, 4, 0, +1/2)

(5, 0, 0, -1/2)

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About This Question

Subject: chemistry
Chapter: atomic structure
Topic: quantum numbers
Difficulty: Medium
Year: 2025

Solution

Correct Answer:

(4, 4, 0, +1/2)

Allowed Ranges:
- $n$ : $1, 2, 3, \dots$
- $l$ : $0$ to $n - 1$
- $m_{l}$ : $- l$ to $+ l$
- $m_{s}$ : $+ 1/2$ or $- 1/2$
Analysis of Option 3: In the set $(4, 4, 0, + 1/2)$ , $n = 4$ and $l = 4$ . Since the maximum value of $l$ is $n - 1 = 3$ , this set is invalid.
Validation of Others:
- (3, 2, -2, +1/2): $l < 3$ and $∣ m_{l} ∣ \leq 2$ . (Valid)
- (2, 1, 0, -1/2): $l < 2$ and $∣ m_{l} ∣ \leq 1$ . (Valid)
- (5, 0, 0, -1/2): $l < 5$ and $m_{l} = 0$ . (Valid)

This medium difficulty chemistry question is from the chapter atomic structure, covering the topic of quantum numbers. It appeared in the 2025 exam.

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