A mineral is made of calcium ,titanium and oxygen `Ca^(2+)` ions located at corners ,`Ti^(4+)` ions at the body -centre and `O^(2-)` ions face -centred of the unit cell. The molecular formula of the mineral is :

Options

A. ` CaTi_(2)O_(3) , +2`
B. `CaTiO_(3), +4 `
C. `CaTi_(3)O_(4) , +2 `
D. ` CaTiO_(2), +2`

Answer

To determine the molecular formula of the mineral composed of calcium, titanium, and oxygen ions, we will analyze the contributions of each type of ion based on their positions in the unit cell.

### Step-by-Step Solution:

1. **Identify the positions of ions in the unit cell:**
- Calcium ions (`Ca^(2+)`) are located at the corners of the unit cell.
- Titanium ions (`Ti^(4+)`) are located at the body center of the unit cell.
- Oxygen ions (`O^(2-)`) are located at the face centers of the unit cell.

2. **Calculate the contribution of `Ca^(2+)` ions:**
- There are 8 corners in a cube.
- Each corner ion contributes `1/8` of an ion to the unit cell because it is shared among 8 unit cells.
- Total contribution from `Ca^(2+)` ions = \( 8 \times \frac{1}{8} = 1 \) ion.

3. **Calculate the contribution of `Ti^(4+)` ions:**
- There is 1 body center in a unit cell.
- The body center ion is not shared with any other unit cell, so its contribution is 1.
- Total contribution from `Ti^(4+)` ions = 1 ion.

4. **Calculate the contribution of `O^(2-)` ions:**
- There are 6 faces in a cube.
- Each face-centered ion contributes `1/2` of an ion to the unit cell because it is shared between 2 unit cells.
- Total contribution from `O^(2-)` ions = \( 6 \times \frac{1}{2} = 3 \) ions.

5. **Summarize the contributions:**
- From the calculations:
- `Ca^(2+)`: 1 ion
- `Ti^(4+)`: 1 ion
- `O^(2-)`: 3 ions

6. **Write the molecular formula:**
- The molecular formula is derived from the contributions of each ion:
- Thus, the molecular formula of the mineral is \( \text{CaTiO}_3 \).

### Final Answer:
The molecular formula of the mineral is \( \text{CaTiO}_3 \).