The edge length of a face centred unit cubic cell is 508 pm. If the radius of cation is 110 pm, the radius of anion will be

Options

A. 110 pm
B. 220 pm
C. 285 pm
D. 144 pm

Explanation

To find the radius of the anion in a face-centered cubic (FCC) unit cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure of FCC Unit Cell**:
- In a face-centered cubic (FCC) unit cell, atoms are located at each of the eight corners and at the centers of each of the six faces of the cube.

2. **Identify the Given Values**:
- Edge length of the unit cell (a) = 508 pm
- Radius of cation (r_cation) = 110 pm

3. **Establish the Relationship**:
- In an FCC unit cell, the relationship between the edge length (a), the radius of the cation (r_cation), and the radius of the anion (r_anion) can be expressed as:
\[ a = 2 \times r_{cation} + 2 \times r_{anion} \]

4. **Substitute the Known Values**:
- Substitute the known values into the equation:
\[ 508 = 2 \times 110 + 2 \times r_{anion} \]

5. **Simplify the Equation**:
- Calculate \(2 \times 110\):
\[ 2 \times 110 = 220 \]
- Now, substitute this back into the equation:
\[ 508 = 220 + 2 \times r_{anion} \]

6. **Isolate the Term with r_anion**:
- Rearranging the equation gives:
\[ 2 \times r_{anion} = 508 - 220 \]
- Calculate \(508 - 220\):
\[ 508 - 220 = 288 \]

7. **Solve for r_anion**:
- Now, divide both sides by 2 to find the radius of the anion:
\[ r_{anion} = \frac{288}{2} = 144 \text{ pm} \]

8. **Final Answer**:
- The radius of the anion is **144 pm**.