A crystalline solid has a cubic structure in which tungsten (W) atoms are located at the cubic corners of the unit cell, oxygen atoms at the edges of the cube and sodium atoms at the cube centre. The molecular formula of the compound is

Options

A. `Na_2WO_3`
B. `NaWO_4`
C. `NaWO_3`
D. `Na_2WO_4`

Explanation

To determine the molecular formula of the crystalline solid described, we will analyze the contributions of tungsten (W), sodium (Na), and oxygen (O) atoms in the unit cell step by step.

### Step 1: Identify the positions of the atoms in the unit cell
- **Tungsten (W) atoms** are located at the corners of the cubic unit cell.
- **Oxygen (O) atoms** are located at the edges of the cube.
- **Sodium (Na) atoms** are located at the center of the cube.

### Step 2: Calculate the contribution of tungsten (W) atoms
- There are **8 corners** in a cubic unit cell.
- Each corner atom contributes **1/8** of its volume to the unit cell because it is shared among 8 unit cells.
- Therefore, the total contribution from tungsten atoms is:
\[ \text{Total W} = 8 \text{ corners} \times \frac{1}{8} = 1 \text{ W atom} \]

### Step 3: Calculate the contribution of sodium (Na) atoms
- There is **1 sodium atom** located at the center of the cube.
- The contribution from the sodium atom is:
\[ \text{Total Na} = 1 \text{ (since it is entirely within the unit cell)} \]

### Step 4: Calculate the contribution of oxygen (O) atoms
- There are **12 edges** in a cubic unit cell.
- Each edge atom contributes **1/4** of its volume to the unit cell because it is shared among 4 unit cells.
- Therefore, the total contribution from oxygen atoms is:
\[ \text{Total O} = 12 \text{ edges} \times \frac{1}{4} = 3 \text{ O atoms} \]

### Step 5: Write the molecular formula
Now that we have the total contributions of each type of atom, we can write the molecular formula:
- From the calculations:
- Tungsten (W) = 1
- Sodium (Na) = 1
- Oxygen (O) = 3

Thus, the molecular formula of the compound is:
\[ \text{NaWO}_3 \]

### Final Answer
The molecular formula of the compound is **NaWO₃**.