Answer:

Fraction of Edge not covered by atoms in FCC unit cell is 0.293 or 29.3%.

Explanation:

FCC unit cell means face-centered cubic unit cell.

In FCC unit cell, there are 4 atoms present at the corners and 1 atom present at the center of each face.

Total number of atoms present in FCC unit cell = 4 corners atoms + 1/2 * 6 face atoms

= 4 + 3 = 7 atoms

Each atom is considered to be present at the corner of a cube.

Let's consider the edge length of the cube to be 'a'.

The length of the face diagonal of the cube = √2a

The length of the body diagonal of the cube = √3a

So, the length of the edge of the cube = a

Fraction of Edge not covered by atoms:

One corner atom contributes to 1/8th of the volume of the cube.

So, the volume of the atom = 1/8 * a^3

Volume of 4 corner atoms = 4 * 1/8 * a^3 = 1/2 * a^3

Volume of 1 face-centered atom = 1/2 * a^2 * (1/4 * √2a) = 1/8 * √2a^3

Total volume of atoms present in the unit cell = 7 * 1/8 * √2a^3 = 7/8 * √2a^3

Fraction of Edge not covered by atoms = Volume of Edge not covered by atoms / Total volume of the cube

Volume of Edge not covered by atoms = Volume of cube - Total volume of atoms present in the unit cell

Volume of cube = a^3

Total volume of atoms present in the unit cell = 7/8 * √2a^3

Volume of Edge not covered by atoms = a^3 - 7/8 * √2a^3

Fraction of Edge not covered by atoms = (a^3 - 7/8 * √2a^3) / a^3

Fraction of Edge not covered by atoms = 1 - 7/8 * √2

Fraction of Edge not covered by atoms = 0.293 or 29.3%

Therefore, the correct answer is option (B) 0.293.