The complex ion `[Fe(CN)_(6)]^(4-)` contains:

Options

A. total of 36 electrons on `Fe^(2+)` cation
B. `sp^(3)d^(2)` hybrid orbitals with octahedral structure
C. total of 104 electrons
D. six sigma bonds

Answer

To solve the question regarding the complex ion \([Fe(CN)_{6}]^{4-}\), we will follow these steps:

### Step 1: Determine the oxidation state of Iron (Fe)
Let the oxidation state of iron be \(x\). The cyanide ion (CN) has a charge of -1, and there are 6 cyanide ions in the complex. The overall charge of the complex is -4.

Using the formula for charge balance:
\[ x + 6(-1) = -4 \]
\[ x - 6 = -4 \]
\[ x = +2 \]

### Step 2: Write the electron configuration of Iron in the +2 oxidation state
The atomic number of iron (Fe) is 26. The electron configuration of neutral iron is:
\[ [Ar] 4s^2 3d^6 \]
For the +2 oxidation state, we remove 2 electrons from the 4s orbital:
\[ Fe^{2+} : [Ar] 3d^6 \]

### Step 3: Analyze the ligand and its effect on electron pairing
Cyanide (CN) is a strong field ligand, which means it will cause electron pairing in the d-orbitals. The 3d orbitals will be filled as follows:
- The 6 electrons in 3d will pair up:
\[ 3d: \uparrow\downarrow \uparrow\downarrow \uparrow\downarrow \]

### Step 4: Determine the hybridization of the complex
Since there are 6 ligands (CN) and the complex is octahedral, the hybridization will be:
\[ d^2sp^3 \]
This indicates that two 3d orbitals, one 4s orbital, and three 4p orbitals are involved in hybridization.

### Step 5: Identify the geometry of the complex
The geometry of the complex ion \([Fe(CN)_{6}]^{4-}\) is octahedral due to the six ligands surrounding the central metal ion.

### Step 6: Determine the magnetic properties of the complex
Since all the electrons in the 3d orbitals are paired, the complex is **diamagnetic**.

### Step 7: Calculate the total number of electrons in the complex
- Contribution from \(Fe^{2+}\): 24 electrons (from \(3d^6\))
- Contribution from 6 cyanide ligands: \(6 \times 2 = 12\) electrons (each CN donates 2 electrons)

Total electrons:
\[ 24 + 12 = 36 \]

### Conclusion
The complex ion \([Fe(CN)_{6}]^{4-}\) contains a total of 36 electrons, has an octahedral geometry, is diamagnetic, and exhibits d2sp3 hybridization.