Question:
Which of the following sets of quantum numbers is not permitted?
Which of the following sets of quantum numbers is not permitted?
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The value of \( l \) must always be less than \( n \), and \( m \) must lie between \( -l \) and \( +l \).
Updated On: Apr 22, 2026
- \( n = 3, l = 3, m = 0, s = \frac{1}{2} \)
- \( n = 3, l = 2, m = +2, s = \frac{-1}{2} \)
- \( n = 3, l = 2, m = -2, s = \frac{-1}{2} \)
- \( n = 3, l = 0, m = 0, s = \frac{1}{2} \)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding quantum numbers.
The four quantum numbers \( n \), \( l \), \( m \), and \( s \) describe the properties of electrons in an atom: - \( n \) is the principal quantum number (n = 1, 2, 3, ...), - \( l \) is the azimuthal quantum number (l = 0 to \( n-1 \)), - \( m \) is the magnetic quantum number (m = -\( l \) to \( l \)), - \( s \) is the spin quantum number (s = \( \pm \frac{1}{2} \)).
Step 2: Analyze the given options.
- (1) \( n = 3, l = 3, m = 0, s = \frac{1}{2} \): This set is not permitted because for \( n = 3 \), the azimuthal quantum number \( l \) must be between 0 and 2, but here \( l = 3 \), which violates the rule. - (2) \( n = 3, l = 2, m = +2, s = \frac{-1}{2} \): This is a valid set of quantum numbers. - (3) \( n = 3, l = 2, m = -2, s = \frac{-1}{2} \): This is also a valid set of quantum numbers. - (4) \( n = 3, l = 0, m = 0, s = \frac{1}{2} \): This is a valid set of quantum numbers.
Step 3: Conclusion.
The correct answer is (1) because \( l \) cannot be equal to 3 when \( n = 3 \).
The four quantum numbers \( n \), \( l \), \( m \), and \( s \) describe the properties of electrons in an atom: - \( n \) is the principal quantum number (n = 1, 2, 3, ...), - \( l \) is the azimuthal quantum number (l = 0 to \( n-1 \)), - \( m \) is the magnetic quantum number (m = -\( l \) to \( l \)), - \( s \) is the spin quantum number (s = \( \pm \frac{1}{2} \)).
Step 2: Analyze the given options.
- (1) \( n = 3, l = 3, m = 0, s = \frac{1}{2} \): This set is not permitted because for \( n = 3 \), the azimuthal quantum number \( l \) must be between 0 and 2, but here \( l = 3 \), which violates the rule. - (2) \( n = 3, l = 2, m = +2, s = \frac{-1}{2} \): This is a valid set of quantum numbers. - (3) \( n = 3, l = 2, m = -2, s = \frac{-1}{2} \): This is also a valid set of quantum numbers. - (4) \( n = 3, l = 0, m = 0, s = \frac{1}{2} \): This is a valid set of quantum numbers.
Step 3: Conclusion.
The correct answer is (1) because \( l \) cannot be equal to 3 when \( n = 3 \).
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