Serway & Jewett — Physics and Measurement: Problem 7

A crystalline solid consists of atoms stacked up in a repeating lattice structure. Consider a crystal as shown in Figure P1.7a. The atoms reside at the corners of cubes of side \( L = 0.200 \text{ nm} \). One piece of evidence for the regular arrangement of atoms comes from the flat surfaces along which a crystal separates, or cleaves, when it is broken. Suppose this crystal cleaves along a face diagonal as shown in Figure P1.7b. Calculate the spacing \( d \) between two adjacent atomic planes that separate when the crystal cleaves.