Which of the following systems has maximum number of unpaired electrons ?

CONCEPT:

Unpaired Electrons in Different Geometries

• The number of unpaired electrons in a coordination complex is determined by the electron configuration of the metal ion and the geometry of the complex (tetrahedral or octahedral).
• In a tetrahedral geometry, the crystal field splitting energy (Δ_t) is lower than in an octahedral geometry. This results in more unpaired electrons because the energy gap between orbitals is smaller, so electrons do not pair up as easily.
• In an octahedral geometry, the crystal field splitting energy (Δ_o) is larger, which can lead to different numbers of unpaired electrons depending on whether the complex is high-spin or low-spin.

EXPLANATION:

• d⁶ (Tetrahedral):
  • In a tetrahedral field, the e orbitals (lower energy) are filled first, followed by the t₂ orbitals (higher energy).
  • For a d⁶ configuration in a tetrahedral field, the electrons will occupy the orbitals as follows: 2 electrons will pair up in the e orbitals, and the remaining 4 electrons will singly occupy the t₂ orbitals.
  • Number of unpaired electrons: 4 unpaired electrons.
• d⁷ (Octahedral, High Spin):
  • In a high-spin octahedral complex, the\( t_{2g}\)orbitals (lower energy) are filled first, followed by the \(e_g\)orbitals (higher energy).
  • For a d⁷ configuration, the electrons will occupy the orbitals as follows: 3 electrons will singly occupy the \(t_{2g}\)orbitals, and the remaining 4 electrons will occupy the \(e_g\) orbitals, with 2 of them being unpaired.
  • Number of unpaired electrons: 3 unpaired electrons.
• d⁴ (Octahedral, Low Spin):
  • In a low-spin octahedral complex, the \(t_{2g}\) orbitals are filled first due to the strong crystal field, which causes the electrons to pair up in the lower energy orbitals before occupying the higher energy \(e_g\) orbitals.
  • For a d⁴ configuration, all 4 electrons will pair up in the \(t_{2g}\) orbitals.
  • Number of unpaired electrons: 2 unpaired electrons.
• d⁹ (Octahedral):
  • In an octahedral field, the \(t_{2g}\) orbitals are filled first, followed by the \(e_g\) orbitals.
  • For a d⁹ configuration, 6 electrons will pair up in the \(t_{2g}\) orbitals, and 3 electrons will occupy the \(e_g\) orbitals, with 1 unpaired electron in the \(e_g\) orbitals.
  • Number of unpaired electrons: 1 unpaired electron.

CONCLUSION:

The correct answer is d⁶ (Tetrahedral) with 4 unpaired electrons.