Which of the following does not represent radius of the atom correctly ?
(i)Simple cubic cell : Radius =`a/2`
(ii)Face centred cubic cell:Radius = `a/(3sqrt3)`
(iii)Body centred cubic cell:Radius =`sqrt3/4a`

Options

A. (i)
B. (iii)
C. (ii)
D. (i) and (ii)

Answer

To determine which of the given statements does not correctly represent the radius of the atom in different types of unit cells, we need to analyze each option based on the geometry of the unit cells.

### Step-by-Step Solution:

1. **Simple Cubic Cell:**
- In a simple cubic cell, the edge length \( a \) is related to the atomic radius \( r \) by the equation:
\[ a = 2r \]
- Rearranging this gives:
\[ r = \frac{a}{2} \]
- Therefore, the statement for the simple cubic cell is correct.

2. **Face-Centered Cubic Cell (FCC):**
- In an FCC unit cell, the edge length \( a \) is related to the atomic radius \( r \) by the equation:
\[ a = 2\sqrt{2}r \]
- Rearranging this gives:
\[ r = \frac{a}{2\sqrt{2}} \]
- The statement given in the question for FCC is:
\[ r = \frac{a}{3\sqrt{3}} \]
- This is incorrect, as we derived \( r = \frac{a}{2\sqrt{2}} \).

3. **Body-Centered Cubic Cell (BCC):**
- In a BCC unit cell, the edge length \( a \) is related to the atomic radius \( r \) by the equation:
\[ a = \frac{4r}{\sqrt{3}} \]
- Rearranging this gives:
\[ r = \frac{\sqrt{3}}{4}a \]
- Therefore, the statement for the body-centered cubic cell is correct.

### Conclusion:
- The only incorrect representation of the atomic radius is for the Face-Centered Cubic cell (FCC). Thus, the answer is:
- **(ii) Face centered cubic cell: Radius = \(\frac{a}{3\sqrt{3}}\)** does not represent the radius of the atom correctly.