A metal 'X' crytallizes in a unit cell in which the radius of atom (r) is related to edge of unit cell (a) as r = 0.3535 a. The total number of atoms present per unit cell is

Explanation

To find the total number of atoms present per unit cell (Z) for the metal 'X' that crystallizes in a unit cell with the given relation between the radius of the atom (r) and the edge length of the unit cell (a), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the Relationship**:
We are given the relationship between the radius of the atom and the edge length of the unit cell:
\[ r = 0.3535a \]

2. **Consider Possible Unit Cell Types**:
There are three common types of unit cells: Simple Cubic (SCC), Body-Centered Cubic (BCC), and Face-Centered Cubic (FCC). Each has a different number of atoms per unit cell:
- SCC: Z = 1
- BCC: Z = 2
- FCC: Z = 4

3. **Check for Simple Cubic (SCC)**:
For a Simple Cubic structure, the relationship between r and a is:
\[ a = 2r \]
Substituting \(r = 0.3535a\) into the SCC equation:
\[ a = 2(0.3535a) \implies a = 0.707a \]
This is not possible, so it cannot be a Simple Cubic structure.

4. **Check for Body-Centered Cubic (BCC)**:
For a Body-Centered Cubic structure, the relationship is:
\[ 4r = \sqrt{3}a \]
We can express this in terms of our given relationship:
\[ 2r = \frac{\sqrt{3}}{2}a \]
Substituting \(r = 0.3535a\):
\[ 2(0.3535a) = \frac{\sqrt{3}}{2}a \implies 0.707a = 0.866a \]
This is also not possible, so it cannot be a Body-Centered Cubic structure.

5. **Check for Face-Centered Cubic (FCC)**:
For a Face-Centered Cubic structure, the relationship is:
\[ 4r = \sqrt{2}a \]
Substituting our relationship:
\[ 4(0.3535a) = \sqrt{2}a \]
Simplifying:
\[ 1.414a = \sqrt{2}a \]
Since both sides are equal, this confirms that the structure is indeed Face-Centered Cubic.

6. **Conclusion**:
Since we have established that the metal 'X' crystallizes in a Face-Centered Cubic structure, the total number of atoms per unit cell (Z) is:
\[ Z = 4 \]

### Final Answer:
The total number of atoms present per unit cell is **4**.