Given n = 2, which of the following quantum numbers is NOT possible for an electron in this shell?

• A. m_l = 0
• B. l = 2
• C. l = 0
• D. l = 1

Answer: (B)

Verified step by step guidance

1. Recall the relationship between the principal quantum number \(n\) and the azimuthal (angular momentum) quantum number \(l\): \(l\) can take integer values from \$0\( up to \)n-1$.
2. Given \(n = 2\), determine the possible values of \(l\). Since \(l\) ranges from \$0\( to \)n-1\(, the allowed values are \)l = 0\( and \)l = 1$.
3. Check each given \(l\) value against the allowed range for \(n=2\). The values \(l=0\) and \(l=1\) are possible, but \(l=2\) is not because it exceeds \(n-1\).
4. Understand that the magnetic quantum number \(m_l\) depends on \(l\) and can take integer values from \(-l\) to \(+l\). For example, if \(l=1\), then \(m_l\) can be \(-1, 0, +1\).
5. Conclude that since \(l=2\) is not allowed for \(n=2\), any quantum number set including \(l=2\) is not possible for an electron in the \(n=2\) shell.