The d-electronic configuration of in tetrahedral crystal field is . Sum of "m" and "number of unpaired electrons" is _________
Show answer and solution
Answer: 7
Solution
Co²⁺ has d⁷ configuration. In a tetrahedral crystal field, the splitting is small (no strong field ligand like Cl⁻), so high spin applies.
Tetrahedral splitting: e level (lower, 2 orbitals) fills first, then t₂ (upper, 3 orbitals).
d⁷ distribution: e⁴ t₂³ → m = 4, n = 3.
Unpaired electrons: e⁴ has 2 unpaired (one pair + two singles? No — 4 electrons in 2 orbitals = 2 paired, 0 unpaired from e? Wait:
e has 2 orbitals → 4 electrons → fully paired → 0 unpaired from e.
t₂ has 3 orbitals → 3 electrons → all unpaired → 3 unpaired.
Total unpaired electrons = 3.
Sum = m + unpaired = 4 + 3 = 7.
Tetrahedral splitting: e level (lower, 2 orbitals) fills first, then t₂ (upper, 3 orbitals).
d⁷ distribution: e⁴ t₂³ → m = 4, n = 3.
Unpaired electrons: e⁴ has 2 unpaired (one pair + two singles? No — 4 electrons in 2 orbitals = 2 paired, 0 unpaired from e? Wait:
e has 2 orbitals → 4 electrons → fully paired → 0 unpaired from e.
t₂ has 3 orbitals → 3 electrons → all unpaired → 3 unpaired.
Total unpaired electrons = 3.
Sum = m + unpaired = 4 + 3 = 7.
[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]