An ionic compound is expected to have body centred type cubic unit cell if `r_(c)//r_(a)`:
(a)lies in range 0.732-1.00
(b)lies in the range of 0.141 to 0.732
(c)lies in the range of 0.255 to 0.414
(d)lies in the range of 0.155 to 0.225

Options

A. lies in range 0.732-1.00
B. lies in the range of 0.141 to 0.732
C. lies in the range of 0.255 to 0.414
D. lies in the range of 0.155 to 0.225

Answer

To determine the range of the radius ratio \( \frac{r_c}{r_a} \) for an ionic compound to have a body-centered cubic (BCC) unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Terms**:
- \( r_c \) is the radius of the cation.
- \( r_a \) is the radius of the anion.
- The ratio \( \frac{r_c}{r_a} \) is crucial in determining the structure of the ionic compound.

2. **Use the Radius Ratio Rule**:
- The radius ratio helps predict the type of packing in ionic compounds. Different ranges of this ratio correspond to different structures:
- **Linear Structure**: \( \frac{r_c}{r_a} < 0.155 \)
- **Triangular Planar Structure**: \( 0.155 < \frac{r_c}{r_a} < 0.225 \)
- **Tetrahedral Structure**: \( 0.225 < \frac{r_c}{r_a} < 0.414 \)
- **Octahedral Structure**: \( 0.414 < \frac{r_c}{r_a} < 0.732 \)
- **Cubic Structures (including BCC)**: \( 0.732 < \frac{r_c}{r_a} < 1.00 \)

3. **Identify the Correct Range for BCC**:
- From the above information, we see that for an ionic compound to exhibit a body-centered cubic structure, the radius ratio \( \frac{r_c}{r_a} \) must lie in the range of \( 0.732 \) to \( 1.00 \).

4. **Select the Correct Option**:
- Given the options:
- (a) \( 0.732 - 1.00 \)
- (b) \( 0.141 - 0.732 \)
- (c) \( 0.255 - 0.414 \)
- (d) \( 0.155 - 0.225 \)
- The correct answer is **(a) \( 0.732 - 1.00 \)**.

### Final Answer:
The ionic compound is expected to have a body-centered cubic unit cell if \( \frac{r_c}{r_a} \) lies in the range **(a) 0.732 - 1.00**.