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) $3p_y$ (ii) $3d_{yz}$
(b) (i) $3p_x$ (ii) $3d_{xy}$
(c) (i) $4s$ (ii) $3d_{xy}$
(d) (i) $3d_{x^2-y^2}$ (ii) $3d_{x^2-y^2}$
Thus, $3d_{x^2-y^2}$ and $3d_{x^2-y^2}$ represents pair of degenerate orbitals.