Which of the following is NOT a valid set of quantum numbers for an electron in an atom?

• A. n = 3, l = 2, m_l = -2, m_s = -1/2
• B. n = 1, l = 1, m_l = 0, m_s = +1/2
• C. n = 4, l = 0, m_l = 0, m_s = -1/2
• D. n = 2, l = 1, m_l = 0, m_s = +1/2

Answer: (B)

Verified step by step guidance

1. Recall the allowed ranges for each quantum number: the principal quantum number \(n\) must be a positive integer (\(n = 1, 2, 3, \ldots\)), the azimuthal quantum number \(l\) can take integer values from \$0\( up to \)n-1\(, the magnetic quantum number \)m_l\( ranges from \)-l\( to \)+l\( in integer steps, and the spin quantum number \)m_s\( can be either \)+\frac{1}{2}\( or \)-\frac{1}{2}$.
2. Check the given quantum numbers one by one to see if they satisfy these rules. For example, for \(n = 1\), \(l\) must be between \$0\( and \)n-1 = 0\(, so \)l\( can only be \)0\( when \)n=1$.
3. Look at the set \(n = 1, l = 1, m_l = 0, m_s = +\frac{1}{2}\). Since \(l\) cannot be equal to or greater than \(n\), this set violates the rule because \(l = 1\) is not allowed when \(n = 1\).
4. Verify the other sets to confirm they follow the rules: for \(n=3, l=2\), \(l\) is less than \(n\), and \(m_l = -2\) is within \(-2\) to \(+2\); for \(n=4, l=0\), \(m_l=0\) is valid; for \(n=2, l=1\), \(m_l=0\) is valid. All these sets are valid.
5. Conclude that the invalid set is the one where \(n=1\) and \(l=1\), because \(l\) must be less than \(n\), making this set not possible for an electron in an atom.