Question

Out of the following pairs of electrons, identify the pairs of electrons present in degenerate orbitals.

• A. (i) $n=3, l=1, m_{l}=-1, m_{s}=-\frac{1}{2}$
  (ii) $n=3, l=2, m_{l}=-1, m_{s}=-\frac{1}{2}$
• B. (i) $n=3, l=1, m_{l}=1, m_{s}=+\frac{1}{2}$
  (ii) $n=3, l=2, m_{l}=1, m_{s}=+\frac{1}{2}$
• C. (i) $n=4, l=1, m_{l}=1, m_{s}=+\frac{1}{2}$
  (ii) $n=3, l=2, m_{l}=1, m_{s}=+\frac{1}{2}$
• D. (i) $n=3, l=2, m_{l}=+2, m_{s}=-\frac{1}{2}$
  (ii) $n=3, l=2, m_{l}=+2, m_{s}=+\frac{1}{2}$

Answer 1

Answer: (D)

Degenerate orbitals means the orbitals of the same subshell of the same main shell, i.e. their $n$ and $l$ values should be same for both the given sets:
(a) (i) $3\, p_{y}$ (ii) $3\, d_{y z}$
(b) (i) $3\, p_{x}$ (ii) $3\, d_{x y}$
(c) (i) $4\, s$ (ii) $3\, d_{x y}$
(d) (i) $3\, d_{x^{2}-y^{2}}$ (ii) $3\, d_{x^{2}-y^{2}}$
Thus, $3\, d_{x^{2}-y^{2}}$ and $3\, d_{x^{2}-y^{2}}$ represents pair of degenerate orbitals.