In ionic solids AB and CD , radius -ratios are x and y respectively. If x +y=0.75 and x-y=0.25 then cations in AB and CD are respectively in

Options

A. T-voids, O-voids
B. O-voids , T-voids
C. T-voids, T-voids
D. O-voids , O-voids

Answer

To solve the problem, we need to find the values of x and y from the given equations and then determine the coordination geometry of the cations in the ionic solids AB and CD.

### Step-by-Step Solution:

1. **Write down the equations:**
We have two equations based on the problem statement:
\[ x + y = 0.75 \quad \text{(1)} \]
\[ x - y = 0.25 \quad \text{(2)} \]

2. **Add the two equations:**
To eliminate y, we can add equations (1) and (2):
\[ (x + y) + (x - y) = 0.75 + 0.25 \]
This simplifies to:
\[ 2x = 1.00 \]

3. **Solve for x:**
Dividing both sides by 2 gives:
\[ x = 0.50 \]

4. **Substitute x back to find y:**
Now, substitute the value of x into equation (1):
\[ 0.50 + y = 0.75 \]
Rearranging gives:
\[ y = 0.75 - 0.50 = 0.25 \]

5. **Summarize the values:**
We have found:
\[ x = 0.50 \quad \text{and} \quad y = 0.25 \]

6. **Determine the coordination geometry:**
- For x = 0.50, we check the range:
- The range for octahedral coordination is between 0.414 and 0.732. Since 0.50 falls within this range, the cation in AB is in an **octahedral** coordination.
- For y = 0.25, we check the range:
- The range for tetrahedral coordination is between 0.225 and 0.414. Since 0.25 falls within this range, the cation in CD is in a **tetrahedral** coordination.

7. **Final answer:**
Therefore, the cations in AB and CD are respectively in **octahedral** and **tetrahedral** coordination.