Calculate the density of silver which crystallizes in face- centred cubic form. The distance between nearest metal atoms is 287 pm (Molar mass of `Ag = 107.87 g mol^(-1) , N_A = 6.022 xx 10^(23) mol^(-1)`).

Explanation

To calculate the density of silver (Ag) which crystallizes in a face-centered cubic (FCC) structure, we can follow these steps:

### Step 1: Understand the relationship between the edge length (A) and the nearest neighbor distance (d).
In an FCC structure, the relationship between the edge length (A) and the nearest neighbor distance (d) is given by:
\[ d = \frac{A}{\sqrt{2}} \]
Given that the nearest metal atom distance \( d \) is 287 pm, we can rearrange this formula to find A:
\[ A = d \cdot \sqrt{2} \]

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