Gold (atoic radius = 0.144 nm) crystallizes in a facelcentred unit cell. What is the length of a side of the cell?

Explanation

To find the length of a side of the face-centered cubic (FCC) unit cell for gold, we can follow these steps:

### Step 1: Understand the structure of the FCC unit cell
In a face-centered cubic unit cell, there are atoms located at each of the eight corners and one atom at the center of each face. The effective radius of the atom can be used to relate the atomic radius to the length of the side of the unit cell.

### Step 2: Use the formula for the side length of the FCC unit cell
The relationship between the atomic radius (R) and the edge length (A) of a face-centered cubic unit cell is given by the formula:
\[ A = 2\sqrt{2}R \]
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