If the atoms are treated as solid spheres,the fraction of volume occupied by the atoms in a body-centered-cubic unit cell is A)0.45 B)0.52 C)0.65 D)0.68 E)0.74

Question

Quizplus · Accepted Answer

In a body-centered cubic unit cell, each atom at the corners is shared among eight unit cells, and there is one atom in the center of the cell. The atom at the center of the cell is a complete sphere that occupies 1/2 of the unit cell volume (since the sphere is centered at the middle of the cube and extends to the corners). The eight corner atoms each occupy 1/8 of the volume of the unit cell, but since they are shared among eight different cells, their total contribution to the unit cell volume is 1. Therefore, the total volume occupied by the atoms in the unit cell is:

(1/2) + 1 = 3/2

The total volume of the unit cell is the cube of the edge length, so the fraction of volume occupied by atoms is:

(3/2) / (a^3) = 0.68   (since a^3 is the volume of the unit cell)

If the Atoms Are Treated as Solid Spheres,the Fraction of Volume