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 with a close-packed structure, we can follow these steps:

### Step 1: Understand the given data
- Density of gold (ρ) = 19.3 g/cm³
- Molar mass of gold (M) = 197 g/mol
- Avogadro's number (Nₑ) = 6.022 × 10²³ atoms/mol
- For a face-centered cubic (FCC) structure, the number of atoms per unit cell (Z) = 4.

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