Crystal Field Theory

CFSE depends on the electronic configuration and the ligand field strength (strong or weak). Strong field ligands create low-spin complexes, while weak field ligands create high-spin complexes.

For strong field ligands (low spin): −1.2Δ₀ + 2P

For weak field ligands (high spin): −0.8Δ₀ − 0.8Δ₀

Step 1: Understanding CFSE.
The Crystal Field Stabilization Energy (CFSE) is the energy stabilization a metal ion experiences due to the ligand field in a coordination complex. It depends on several factors:

Step 2: Factors Affecting CFSE.
- (A) The nature of the ligand: Different ligands cause different splitting of d-orbitals, affecting the overall CFSE. Strong field ligands cause a larger splitting and higher CFSE. - (B) The charge on the metal ion: The higher the charge on the metal ion, the stronger the electrostatic attraction between the metal and the ligands, leading to a higher CFSE. - (C) The position of the metal ion in the transition series: As we move across the transition series, the d-orbital splitting increases, which leads to higher CFSE. - (D) Geometry of the complex: While geometry influences the overall ligand field strength, it doesn't directly determine the magnitude of CFSE.

Step 3: Conclusion.
Thus, the correct answer is option (1): (A), (B) and (C) only.

Step 1: Understanding CFSE for Octahedral Complexes.
The Crystal Field Stabilization Energy (CFSE) for an octahedral complex is calculated using the formula: where is the octahedral crystal field splitting energy.

Step 2: Applying the Formula to Configuration.
For a configuration in an octahedral field, the electron arrangement will have 2 electrons in the higher-energy -orbitals and 6 electrons in the lower-energy -orbitals. The CFSE for such a configuration is:

Step 3: Conclusion.
Thus, the CFSE for the octahedral ion is -0.4 , corresponding to option (1).

Step 1: Understanding Ligand Field Strength.
The strength of the ligand field influences the d-orbital splitting in transition metal complexes. Strong field ligands cause a large splitting of the d-orbitals, while weak field ligands cause a smaller splitting. The ligand field strength follows the trend:

Step 2: Analyzing the Ligands.
- (A) NH is a weak field ligand. - (B) C O (oxalate) is a moderate field ligand. - (C) OH is a weaker field ligand compared to NH . - (D) CN is a strong field ligand, causing the largest splitting.

Step 3: Conclusion.
Thus, the order of increasing d-orbital splitting is: So, the correct answer is option (4): (C), (B), (A), (D).