Question

4.5 quantization and quantum numbers
which of the following sets of quantum numbers would correctly identify an electron in the 3p subshell?
o n=3, l=3, m_l=0, m_s=+1/2
o n=3, l=2, m_l=0, m_s=-1/2
o n=3, l=1, m_l=-1, m_s=+1/2
o n=3, l=1, m_l=-2, m_s=-1/2

Explanation:

Step1: Recall quantum - number rules for subshell

For a given shell \(n\), the angular - momentum quantum number \(l\) has values \(l = 0,1,\cdots,n - 1\). For the \(p\) subshell, \(l=1\). The magnetic quantum number \(m_l\) has values \(m_l=-l,-l + 1,\cdots,0,\cdots,l-1,l\), and the spin quantum number \(m_s=\pm\frac{1}{2}\).

Step2: Analyze each option for \(n = 3\) and \(p\) sub - shell (\(l = 1\))

For an electron in the \(3p\) subshell, \(n = 3\) and \(l = 1\).

• Option 1: \(n = 3\), \(l = 3\) is incorrect since for \(n = 3\), \(l\) can be \(0,1,2\) but not \(3\).
• Option 2: \(n = 3\), \(l = 2\) is incorrect as for \(3p\), \(l = 1\).
• Option 3: \(n = 3\), \(l = 1\), \(m_l=-1\) (since \(m_l\) for \(l = 1\) can be \(- 1,0,1\)) and \(m_s=\frac{1}{2}\) is correct.
• Option 4: \(n = 3\), \(l = 1\), but \(m_l=-2\) is incorrect because for \(l = 1\), \(m_l\) values range from \(-1\) to \(1\).

Answer:

C. \(n = 3\), \(l = 1\), \(m_l=-1\), \(m_s=+\frac{1}{2}\)