Metallic gold crystallizes in the face-centred cubic lattice. The edge length of the cubic unit cell, a = 4.070 A. Calculate the closest distance between gold atoms and the density of gold. Atomic mass of Au = 197 amu.

Explanation

To solve the problem, we will calculate the closest distance between gold atoms and the density of gold using the given information.

### Step 1: Calculate the closest distance between gold atoms

In a face-centered cubic (FCC) lattice, the closest distance between the atoms can be calculated using the formula:

\[
d = \frac{\sqrt{2}}{2} a
...