If the unit cell of copper has an edge length of approximately 362 pm and the radius of a copper atom is approximately 128 pm,what is copper's probable crystal structure?

Question

Quizplus · Accepted Answer

The radius of a copper atom is approximately 128 pm, and the edge length of the unit cell is approximately 362 pm. To find the crystal structure, we must compare the ratio of the atomic radius to the edge length with the corresponding ratios for the different crystal structures.

For a simple cubic structure, the ratio of the atomic radius to the edge length is 0.353, which is lower than the ratio for copper. For a side-centered cubic structure, the ratio is 0.414, which is still lower than the ratio for copper. For a body-centered cubic structure, the ratio is 0.68, which is higher than the ratio for copper. The only option left is the face-centered cubic structure, for which the ratio is 0.74, which is the closest to the ratio of copper. Therefore, the probable crystal structure for copper is face-centered cubic.

If the Unit Cell of Copper Has an Edge Length