Nickel crystallizes in a face-centered cubic array of atoms, and the length of the unit cell edge is 351 pm . What is the radius of the nickel atom?
Strategy

On one face of this cell there are five nickel atoms—one at each corner and one in the center of the face. Since we assume that each atom is a sphere, the three atoms along the face diagonal must be in contact with each other, so the length of the face diagonal is four times the radius of a nickel atom:

Because the diagonal of the face of the unit cell is the hypotenuse of a right triangle in which each of the legs is equal to the length of the edge of the unit cell a, we can use the Pythagorean theorem (the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse) to fi nd the length of the diagonal in terms of the edge length.

Transcribed Image Text:

Length of diagonal = 4 x r