Question

A solid has a structure in which W atoms are located at the corners of the unit cell, O atoms are located at the cube edges, and Na atoms at the cube centre. The formula of the compound is:

• A. Na$_2$WO$_3$
• B. NaWO$_3$
• C. Na$_2$W$_2$O$_4$
• D. Na$_2$WO$_6$

Hint:

Corner atoms contribute $\tfrac{1}{8}$, edge atoms $\tfrac{1}{4}$, face-centre atoms $\tfrac{1}{2}$, and body-centre atoms contribute \textbf{1} to a unit cell.

Answer 1

The Correct Option is B

Step 1: Calculate the contribution of W atoms. W atoms are present at the 8 corners of the unit cell. Each corner atom contributes $\dfrac{1}{8}$. \[ \text{Total W atoms} = 8 \times \frac{1}{8} = 1 \]
Step 2: Calculate the contribution of O atoms. O atoms are present at the 12 edges of the cube. Each edge atom contributes $\dfrac{1}{4}$. \[ \text{Total O atoms} = 12 \times \frac{1}{4} = 3 \]
Step 3: Calculate the contribution of Na atoms. Na atoms are present at the body centre of the cube. Each body-centred atom contributes 1. \[ \text{Total Na atoms} = 1 \]
Step 4: Write the formula using the obtained ratio: \[ \text{Na : W : O} = 1 : 1 : 3 \]
Step 5: Therefore, the formula of the compound is: \[ \boxed{\text{NaWO}_3} \]