What is the maximum number of layers of atom in close-packed planes that will lie within two imaginary parallel planes having a distance between them of `13sqrt((2)/(3))r` (where `r` is the radius of atom) in the copper crystal (fcc)?
(Consider the atoms to be within the parallel planes if their centres are on or within the two parallel planes).

Options

A. 5
B. 6
C. 7
D. 8

Explanation

To solve the problem, we need to determine the maximum number of layers of atoms in close-packed planes that can fit between two parallel planes separated by a distance of \( 13\sqrt{\frac{2}{3}}r \), where \( r \) is the radius of the atom in a face-centered cubic (FCC) structure.

### Step-by-Step Solution:

1. **Understanding the FCC Structure**:
In a face-centered cubic (FCC) structure, the atoms are arranged such that there are layers of atoms stacked in a close-packed manner. The distance between two adjacent close-packed planes (layers) can be calculated.

2. **Distance Between Close-Packed Planes**:
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