To determine how many of the given statements are correct, we will analyze each statement one by one based on the information provided in the video transcript.
### Statement Analysis:
1. **Statement A**: The order of splitting energy is \( \text{PtCl}_4^{2-} > \text{PdCl}_4^{2-} > \text{NiCl}_4^{2-} \).
- **Analysis**: The statement claims a specific order of splitting energy based on the magnitude. However, the transcript indicates that the splitting energy (Δ₀) is the same for these complexes when considering only the magnitude. Therefore, this statement is **incorrect**.
2. **Statement B**: \( \text{Ni(CO)}_4 \) is diamagnetic.
- **Analysis**: The configuration of nickel in \( \text{Ni(CO)}_4 \) is \( 3d^8 4s^2 \). Since CO is a strong field ligand, it causes pairing of electrons, leading to a completely filled \( 3d \) subshell. Thus, \( \text{Ni(CO)}_4 \) is indeed diamagnetic. Therefore, this statement is **correct**.
3. **Statement C**: \( \text{Ni(H}_2\text{O})_6^{2+} \) is paramagnetic.
- **Analysis**: In \( \text{Ni(H}_2\text{O})_6^{2+} \), nickel is in the +2 oxidation state, resulting in a \( 3d^8 \) configuration. Since water is a weak field ligand, it does not cause pairing of electrons. Therefore, there are unpaired electrons, making it paramagnetic. This statement is **correct**.
4. **Statement D**: The magnetic moment of \( \text{K}_3[\text{Fe(CN)}_6] \) is \( \sqrt{3} \, \text{BM} \).
- **Analysis**: In \( \text{K}_3[\text{Fe(CN)}_6] \), iron is in the +3 oxidation state, resulting in a \( 3d^5 \) configuration. Since CN is a strong field ligand, it causes pairing of electrons. In this case, there will be only one unpaired electron remaining. The magnetic moment is calculated as \( \sqrt{n(n+2)} \) where \( n \) is the number of unpaired electrons. Here, \( n = 1 \), leading to \( \sqrt{1(1+2)} = \sqrt{3} \, \text{BM} \). Thus, this statement is **correct**.
### Summary of Statements:
- Statement A: Incorrect
- Statement B: Correct
- Statement C: Correct
- Statement D: Correct
### Conclusion:
Out of the four statements, **three statements (B, C, and D) are correct**.
### Final Answer:
**3 statements are correct.**
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