What is the edge length of a face-centered cubic unit cell made up of atoms having a radius of 175 pm

495 pm (see the relationship between the edge length (a) and radius (r) of atoms in attachment).

Explanation:

A crystalline solid possess rigid and long-range order; its atoms, molecules, or ions occupy specific positions. A unit cell is the basic repeating structural unit of a crystalline solid. Each sphere in the unit cell represents an atom, ion, or molecule and is called a lattice point. The way the spheres are arranged in layers determines what type of unit cell we have.

In the face-centered cubic cell, there are spheres at the center of each of the six faces of the cube, in addition to the eight corner spheres (see the second picture in the attachment). Each sphere in this arrangement is said to have a coordination number of 12 since each sphere is in contact with six spheres in its own layer, three spheres in the layer above, and three spheres in the layer below. The coordination number is defined as the number of atoms (or ions) surrounding an atom (or ion) in a crystal lattice.

In the first picture in the attachment we can see that the relationship between the atomic radius r and the  edge length a face-centered  cubic cell is:

a=√8*r

Therefore, the edge length will be √8*175 pm = 495 pm

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