Question

consider borons electron configuration of 1s² 2s² 2p¹. which of the follow would not be a good set of quantum numbers to write for the electron in the 2p subshell? 2, 1, 1, +1/2 2, 0, 0, +1/2 2, 1, 0, -1/2 2, 1, -1, -1/2

Explanation:

For an electron in the \(2p\) sub - shell:

• The principal quantum number \(n = 2\) (since it is in the second shell).
• The azimuthal quantum number \(l\) for \(p\) sub - shell is \(l = 1\) (because \(l=0\) for \(s\), \(l = 1\) for \(p\), \(l=2\) for \(d\) etc.).
• The magnetic quantum number \(m_l\) has values \(m_l=-l,-l + 1,\cdots,l\). So for \(l = 1\), \(m_l=-1,0,1\).
• The spin quantum number \(m_s=\pm\frac{1}{2}\)

Let's check each option:

• Option \([2,1,1,+\frac{1}{2}]\): \(n = 2\), \(l = 1\), \(m_l=1\) (valid as \(m_l=-1,0,1\) for \(l = 1\)), \(m_s=+\frac{1}{2}\) (valid).
• Option \([2,0,0,+\frac{1}{2}]\): Here \(l = 0\) which corresponds to \(s\) sub - shell, not \(p\) sub - shell (\(p\) has \(l = 1\)).
• Option \([2,1,0,-\frac{1}{2}]\): \(n = 2\), \(l = 1\), \(m_l = 0\) (valid as \(m_l=-1,0,1\) for \(l = 1\)), \(m_s=-\frac{1}{2}\) (valid).
• Option \([2,1,-1,-\frac{1}{2}]\): \(n = 2\), \(l = 1\), \(m_l=-1\) (valid as \(m_l=-1,0,1\) for \(l = 1\)), \(m_s=-\frac{1}{2}\) (valid).

Answer:

\([2,0,0,+\frac{1}{2}]\)