A solid has a structure in which `W` atoms are located at the corners of a cubic lattice, `O` atom at the centre of edges, and `Na` atom at the centre of the cube. The formula for the compound is

Options

A. `NaWO_(2)`
B. `NaWO_(3)`
C. `Na_(2)WO_(3)`
D. `NaWO_(4)`

Explanation

To determine the formula of the compound based on the given structure, we will follow these steps:

### Step 1: Identify the position and contribution of W atoms
- W atoms are located at the corners of the cubic lattice.
- In a cubic lattice, there are 8 corners.
- Each corner atom contributes \( \frac{1}{8} \) of an atom to the unit cell.

**Calculation:**
\[ \text{Number of W atoms} = 8 \times \frac{1}{8} = 1 \]

### Step 2: Identify the position and contribution of O atoms
- O atoms are located at the center of the edges of the cube.
- A cube has 12 edges.
- Each edge atom contributes \( \frac{1}{4} \) of an atom to the unit cell.

**Calculation:**
\[ \text{Number of O atoms} = 12 \times \frac{1}{4} = 3 \]

### Step 3: Identify the position and contribution of Na atoms
- Na atoms are located at the center of the cube (body center).
- There is only 1 body center atom, and it contributes fully to the unit cell.

**Calculation:**
\[ \text{Number of Na atoms} = 1 \]

### Step 4: Write the formula of the compound
- Now we can combine the contributions of each atom to write the formula.
- From our calculations, we have:
- 1 W atom
- 3 O atoms
- 1 Na atom

**Formula:**
\[ \text{Formula of the compound} = \text{Na}_1\text{W}_1\text{O}_3 = \text{NaWO}_3 \]

### Conclusion
The formula for the compound is **NaWO3**.

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