Question

The conditions and consequences that favour the \( t_{2g}^3 e_g^1 \) configuration in a metal complex are:

• A. Weak field ligand, low spin complex
• B. Strong field ligand, low spin complex
• C. Strong field ligand, high spin complex
• D. Weak field ligand, high spin complex

Hint:

The strength of the field ligand influences the distribution of electrons between \( t_{2g} \) and \( e_g \) orbitals. Weak field ligands lead to high spin configurations, while strong field ligands lead to low spin configurations.

Answer 1

The Correct Option is A

The \( t_{2g}^3 e_g^1 \) configuration is typical for a weak field ligand. In such cases, the electrons tend to occupy the higher energy \( e_g \) orbitals, as opposed to pairing up in the lower energy \( t_{2g} \) orbitals. This leads to a low spin complex. 
Final Answer: Weak field ligand, low spin complex.

Answer 2

Step 1: Understand the electronic configuration of metal complexes.
In a metal complex, the d-orbitals of the metal ion split into two sets of orbitals: \( t_{2g} \) (lower energy) and \( e_g \) (higher energy). The electron configuration for a \( d^4 \) complex, for example, can be \( t_{2g}^3 e_g^1 \), where 3 electrons occupy the lower energy \( t_{2g} \) orbitals, and 1 electron occupies the higher energy \( e_g \) orbital.

The distribution of electrons between these orbitals is influenced by the nature of the ligands. In the case of weak field ligands, the splitting between the \( t_{2g} \) and \( e_g \) orbitals is relatively small, and electrons are more likely to occupy higher energy orbitals. This leads to a configuration like \( t_{2g}^3 e_g^1 \), which is commonly seen in low spin complexes.

Step 2: Conditions favoring the \( t_{2g}^3 e_g^1 \) configuration.
- Weak field ligands: These ligands do not cause a large splitting of the d-orbitals, meaning the energy difference between the \( t_{2g} \) and \( e_g \) orbitals is small. As a result, electrons will occupy both sets of orbitals (with one electron in the \( e_g \) orbital) to minimize electron repulsion, leading to a low spin configuration.
- Low spin complex: In a low spin complex, the splitting energy is not large enough to force all electrons into the lower \( t_{2g} \) orbitals, so electrons fill both the \( t_{2g} \) and \( e_g \) orbitals, leading to the \( t_{2g}^3 e_g^1 \) configuration.

Step 3: Conclusion.
The \( t_{2g}^3 e_g^1 \) configuration is favored by weak field ligands and is characteristic of low spin complexes.

Final Answer:
\[ \boxed{\text{Weak field ligand, low spin complex}}. \]