Which of the following is not a condition for complex formation?

Options

A. Small atomic size
B. High nuclear charge
C. Variable oxidation state
D. Availability of vacant d-orbitals

Answer

To solve the question "Which of the following is not a condition for complex formation?" we need to analyze the options provided and understand the conditions required for complex formation, particularly in transition metals.

### Step-by-Step Solution:

1. **Understanding Complex Formation**:
- Complex formation primarily occurs with transition metal ions. These ions can form complex compounds by coordinating with ligands, which can be anions or neutral molecules that have lone pairs of electrons.

2. **Identifying Conditions for Complex Formation**:
- There are three main conditions that facilitate complex formation:
- **Smaller Size of Ions**: Transition metal ions typically have a smaller ionic radius which allows them to effectively interact with ligands.
- **Higher Ionic Charge**: Transition metals often exhibit higher oxidation states, which increases their charge density and enhances their ability to attract ligands.
- **Availability of Vacant d-Orbitals**: Transition metals have vacant d-orbitals that can accept lone pairs of electrons from ligands.

3. **Evaluating the Options**:
- We need to evaluate the options given in the question to identify which one does not fit the criteria for complex formation. The key point to remember is that while variable oxidation states are common in transition metals, they are not a necessary condition for complex formation.

4. **Conclusion**:
- Among the options, the one that states "variable oxidation state" is **not a condition for complex formation**. Transition metals can form complexes even if they do not exhibit variable oxidation states.

### Final Answer:
The option that is **not a condition for complex formation** is **variable oxidation state**.