If radius of a metal atom (A) is 5pm and radius of an electronegative atom (B) is 20 pm, then in the unit cell

Options

A. A in octahedral voids, B in FCC unit
B. A in FCC unit, B in tetrahedral void
C. A in BCC unit, B in cubic void
D. A in tetrahedral void, B in FCC unit

Answer

To solve the problem, we need to determine the type of unit cell formed by the metal atom (A) and the electronegative atom (B) based on their given radii.

### Step-by-Step Solution:

1. **Identify the Radii**:
- The radius of metal atom A = 5 pm
- The radius of electronegative atom B = 20 pm

2. **Calculate the Radius Ratio**:
- The radius ratio (r⁺/r⁻) is calculated as follows:
\[ \text{Radius Ratio} = \frac{r^+}{r^-} = \frac{5 \text{ pm}}{20 \text{ pm}} = 0.25 \]

3. **Determine the Coordination Number**:
- According to the radius ratio rule:
- If the radius ratio is between 0.115 and 0.225, the coordination number is 4 (tetrahedral voids).
- If the radius ratio is between 0.225 and 0.414, the coordination number is 4 (tetrahedral voids).
- Since 0.25 falls in the range of 0.225 to 0.414, the coordination number is 4.

4. **Identify the Type of Unit Cell**:
- A coordination number of 4 indicates that the arrangement is tetrahedral.
- In a tetrahedral arrangement, the smaller cation (A) will occupy the tetrahedral voids, while the larger anion (B) will form the lattice.

5. **Determine the Packing**:
- The packing arrangement is typically face-centered cubic (FCC) for larger anions (B) with smaller cations (A) fitting into the tetrahedral voids.
- Therefore, the unit cell formed is an FCC structure with cation A in the tetrahedral voids.

6. **Final Conclusion**:
- The unit cell is an FCC unit cell with cation A (5 pm) in the tetrahedral voids and anion B (20 pm) forming the lattice.