What is the geometrical shape of complex and hybridisation of central metal in `[Fe(CO)_5]` ?

Options

A. Tetrahedral, `sp^3`
B. Square planar, `dsp^2`
C. Trigonal bipyramidal, `dsp^3`
D. Trigonal bipyramidal, `sp^3d`

Answer

To determine the geometrical shape and hybridization of the central metal in the complex \([Fe(CO)_5]\), we can follow these steps:

### Step 1: Identify the oxidation state of Iron (Fe)
- The ligand CO (carbon monoxide) is a neutral ligand, meaning it does not contribute any charge.
- Therefore, the oxidation state of Fe in \([Fe(CO)_5]\) is 0.

### Step 2: Determine the electronic configuration of Iron
- The atomic number of iron (Fe) is 26. Its electronic configuration is:
\[ [Ar] 4s^2 3d^6 \]

### Step 3: Analyze the effect of the ligand
- CO is a strong field ligand, which means it will cause the pairing of electrons in the d-orbitals.
- In the case of Fe, the 3d electrons will pair up, leading to the following configuration:
\[ 3d^6 \rightarrow \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \quad (6 \text{ electrons paired}) \]
- The 4s orbital remains filled with 2 electrons:
\[ 4s^2 \]

### Step 4: Determine the hybridization
- Since there are 5 CO ligands, they will coordinate with the central metal (Fe) and require hybridization.
- The hybridization can be determined by the number of orbitals involved:
- 3d, 4s, and 4p orbitals are involved in bonding.
- The hybridization is therefore \(dsp^3\).

### Step 5: Identify the geometrical shape
- The \(dsp^3\) hybridization corresponds to a trigonal bipyramidal geometry.
- In this arrangement, three ligands occupy the equatorial positions and two occupy the axial positions.

### Conclusion
- The hybridization of the central metal (Fe) in \([Fe(CO)_5]\) is \(dsp^3\).
- The geometrical shape of the complex is trigonal bipyramidal.

### Final Answer
- **Hybridization:** \(dsp^3\)
- **Geometrical Shape:** Trigonal bipyramidal