How many electrons are present in d-orbitals which are present along the axis in `[Ti(H_(2)O)_(6)]^(3+)` ? .

Answer

To determine how many electrons are present in the d-orbitals that are aligned along the axis in the coordination complex \([Ti(H_2O)_6]^{3+}\), we can follow these steps:

### Step 1: Determine the oxidation state of Titanium
1. The complex is \([Ti(H_2O)_6]^{3+}\).
2. The charge of the complex is \(+3\).
3. The ligand \(H_2O\) is neutral (0 charge).
4. Let the oxidation state of Titanium be \(x\).
5. The equation can be set up as:
\[ x + 6(0) = +3 \implies x = +3 \]
Thus, Titanium is in the +3 oxidation state.

### Step 2: Write the electron configuration of Titanium
1. The atomic number of Titanium (Ti) is 22.
2. The ground state electron configuration of Titanium is:
\[ [Ar] 4s^2 3d^2 \]

### Step 3: Adjust the electron configuration for the +3 oxidation state
1. When Titanium loses 3 electrons to form \(Ti^{3+}\), it loses the 2 electrons from the 4s orbital and 1 electron from the 3d orbital.
2. Therefore, the electron configuration for \(Ti^{3+}\) is:
\[ [Ar] 3d^1 \]

### Step 4: Identify the d-orbitals and their orientations
1. The d-orbitals consist of five orbitals: \(d_{xy}\), \(d_{yz}\), \(d_{zx}\), \(d_{x^2-y^2}\), and \(d_{z^2}\).
2. The orbitals \(d_{x^2-y^2}\) and \(d_{z^2}\) are aligned along the axes.

### Step 5: Determine the occupancy of d-orbitals along the axis
1. In the \(Ti^{3+}\) configuration, there is only 1 electron in the 3d orbitals.
2. The electron will occupy one of the d-orbitals, but it will not occupy the axial orbitals \(d_{x^2-y^2}\) or \(d_{z^2}\) since it will fill the lower energy orbitals first, which are \(d_{xy}\), \(d_{yz}\), or \(d_{zx}\).
3. Therefore, the number of electrons in the d-orbitals along the axis (\(d_{x^2-y^2}\) and \(d_{z^2}\)) is:
\[ 0 \]

### Final Answer
The number of electrons present in the d-orbitals that are aligned along the axis in \([Ti(H_2O)_6]^{3+}\) is **0**.

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