The correct statement (s) regarding the binary transition metal carbonyl compounds is (are)
(Atomic numbers: Fe = 26, Ni = 28)

Options

A. Total number of valence shell electrons at metal centre in `Fe(CO)_(5) or Ni(CO)_(4)` is 6
B. These are predominantly low spin in the nature
C. Metal- carbon bond strengthens when the oxidation state of the metal is lowered
D. The carbonyl C-O bond weakens when the oxidation state of the metal is increased

Answer

To solve the question regarding the correct statements about binary transition metal carbonyl compounds, we will analyze the statements one by one based on the information provided in the video transcript.

### Step-by-Step Solution:

1. **Identify the Valence Electrons in Iron Carbonyl (Fe(CO)5)**:
- Iron (Fe) has an atomic number of 26. Its ground state electronic configuration is \( [Ar] 3d^6 4s^2 \).
- In the complex Fe(CO)5, carbonyl (CO) is a neutral ligand, so the oxidation state of iron is 0.
- Therefore, the total number of valence electrons in iron is \( 6 (from 3d) + 2 (from 4s) = 8 \) valence electrons.

2. **Identify the Valence Electrons in Nickel Carbonyl (Ni(CO)4)**:
- Nickel (Ni) has an atomic number of 28. Its ground state electronic configuration is \( [Ar] 3d^8 4s^2 \).
- In the complex Ni(CO)4, carbonyl (CO) is also a neutral ligand, so the oxidation state of nickel is 0.
- Thus, the total number of valence electrons in nickel is \( 8 (from 3d) + 2 (from 4s) = 10 \) valence electrons.

3. **Evaluate the Spin State of the Complexes**:
- Carbonyl (CO) is a strong field ligand according to the spectrochemical series.
- Strong field ligands tend to produce low spin complexes.
- Therefore, the statement that these complexes are predominantly low spin is **correct**.

4. **Analyze the Strength of Metal-Carbon Bond with Oxidation State**:
- When the oxidation state of the metal decreases, the tendency of the metal to donate electron pairs to the carbonyl ligand increases.
- This leads to increased synergic bonding, which strengthens the metal-carbon bond.
- Thus, the statement that the metal-carbon bond strengthens when the oxidation state of the metal is lowered is **correct**.

5. **Evaluate the Effect of Increased Oxidation State on Carbonyl Bond**:
- When the oxidation state of the metal increases, the tendency to donate electron pairs decreases, leading to decreased synergic bonding.
- This means that the carbon-oxygen bond remains strong because there is less addition of electrons to the anti-bonding orbitals.
- Therefore, the statement that the carbonyl bond weakens when the oxidation state of the metal is increased is **incorrect**.

### Conclusion:
Based on the analysis:
- The **correct statements** regarding binary transition metal carbonyl compounds are:
- They are predominantly low spin in nature.
- The metal-carbon bond strengthens when the oxidation state of the metal is lowered.