Gold has a close-packed structure which can be viewed as-spheres occupying 0.74 of the total volume. If the density of gold is 19.3 g/cc, calculate the apparent radius of a gold ion in the solid

Explanation

To calculate the apparent radius of a gold ion in a solid state, we can follow these steps:

### Step 1: Understand the Structure and Given Data
Gold has a close-packed structure, specifically a face-centered cubic (FCC) structure. The packing fraction of this structure is given as 0.74, and the density of gold is provided as 19.3 g/cm³.

### Step 2: Determine the Number of Atoms in the Unit Cell
In an FCC structure:
- There are 8 corner atoms, each contributing \( \frac{1}{8} \) of an atom.
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