Question

1. ** which set of quantum numbers depicts an electron in a \d\ subshell?

a. n=3, l=2, m_l=1, m_s=1/2
b. n=4, l=1, m_l=0, m_s=1/2
c. n=2, l=0, m_l=0, m_s=-1/2
d. n=5, l=3, m_l=2, m_s=1/2

Explanation:

• The principal quantum number \(n\) represents the energy level.
• The angular - momentum quantum number \(l\) determines the subshell: \(l = 0\) (s - subshell), \(l=1\) (p - subshell), \(l = 2\) (d - subshell), \(l=3\) (f - subshell).
• For option A: \(n = 3\), \(l = 2\) (d - subshell), \(m_l=1\) (magnetic quantum number, which gives the orbital within the subshell), \(m_s=\frac{1}{2}\) (spin quantum number).
• For option B: \(l = 1\) corresponds to a p - subshell.
• For option C: \(l = 0\) corresponds to an s - subshell.
• For option D: \(l = 3\) corresponds to an f - subshell.

Answer:

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