Platinum (atomic radius `= 1.38 Å`) crystallises in a cubic closed packed structure. Calculate the edge length of the face-centred cubic unit cell and the density of the platinum (Pt = 195)

Explanation

To solve the problem, we need to calculate the edge length of the face-centered cubic (FCC) unit cell and the density of platinum (Pt).

### Step 1: Calculate the Edge Length of the FCC Unit Cell

1. **Understanding the FCC Structure**: In a face-centered cubic (FCC) structure, atoms are located at each corner of the cube and at the center of each face. Each corner atom contributes 1/8 of its volume to the unit cell, and each face-centered atom contributes 1/2.

2. **Relationship Between Atomic Radius and Edge Length**: In an FCC structure, the face diagonal can be expressed in terms of the atomic radius (r). The face diagonal (d) can be calculated as:
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