By X-ray studies, the packing atoms, in a crystal of gold is found to be in layers such that starting from any layer, every fourth layer is found to be exactly idenctical. The density of gold is found to be ` 19.4 g cm^(-3)` and its atomic mass is 197 a.m.u.
The length of the edge of the unit cell will be

Options

A. 407 pm
B. 189 pm
C. 814 pm
D. 204 pm

Explanation

To find the length of the edge of the unit cell of gold, we can use the relationship between density, atomic mass, and the unit cell volume. Here’s a step-by-step solution:

### Step 1: Understand the structure of gold
Gold crystallizes in a face-centered cubic (FCC) structure, which means:
- The coordination number (Z) is 12.
- Each unit cell contains 4 atoms (Z = 4).

### Step 2: Use the density formula
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