Using valence bond theory , the complex `[Cr(H_(2)O)_(6)]^(3+)` can be described as

Options

A. `sp^(3) d^(2)` , outer orbital complex , paramagnetic
B. `dsp^(2)` , inner orbital complex , diamagnetic
C. `d^(2) sp^(3)` , inner orbital complex , paramagnetic
D. `d^(2) sp^(3)` , outer orbital complex , diamagnetic .

Explanation

To describe the complex \([Cr(H_2O)_6]^{3+}\) using valence bond theory (VBT), we can follow these steps:

### Step 1: Determine the oxidation state of chromium
The complex has a total charge of +3. The ligands (water, \(H_2O\)) are neutral. Let \(X\) be the oxidation state of chromium.

\[ X + 6 \times 0 = +3 \implies X = +3 \]

### Step 2: Write the electronic configuration of chromium
The atomic number of chromium (Cr) is 24. The ground state electronic configuration is:

\[ [Ar] 3d^5 4s^1 \]

### Step 3: Adjust the electronic configuration for the +3 oxidation state
When chromium is in the +3 oxidation state, it loses three electrons. The electrons are removed first from the 4s orbital and then from the 3d orbital:

\[ 3d^5 4s^1 \rightarrow 3d^3 4s^0 \]

Thus, the electronic configuration of \(Cr^{3+}\) is:

\[ 3d^3 \]

### Step 4: Analyze the ligand and its effect on pairing
The ligand \(H_2O\) is a weak field ligand, which means it does not cause pairing of the d-electrons. Therefore, the three electrons in the \(3d\) subshell remain unpaired:

\[ 3d: \uparrow \quad \uparrow \quad \uparrow \]

### Step 5: Determine the hybridization
The coordination number of the complex is 6, which indicates that 6 orbitals are involved in bonding. The orbitals involved in hybridization for this complex are:

- 2 from the \(3d\) subshell
- 1 from the \(4s\) subshell
- 3 from the \(4p\) subshell

Thus, the hybridization can be described as:

\[ d^2sp^3 \]

### Step 6: Determine the magnetic properties
Since there are three unpaired electrons in the \(3d\) subshell, the complex is paramagnetic.

### Step 7: Classify the type of complex
Since we used the \(3d\) orbitals for hybridization, this complex is classified as an inner orbital complex.

### Final Description
Using valence bond theory, the complex \([Cr(H_2O)_6]^{3+}\) can be described as:
- Hybridization: \(d^2sp^3\)
- Magnetic nature: Paramagnetic
- Type of complex: Inner orbital complex