Material Science Exam 1 Practice Test

In a simple cubic lattice, the lattice parameter a relates to the atomic radius R by which expression?

a = 4R a = 2R a = √3 R a = R

Correct Answer:

a = 2R

Explanation:

In a simple cubic lattice, the lattice parameter a is the edge length of the cube. Along that edge, atoms at adjacent corners touch each other, so the center-to-center distance between those touching atoms is 2R. Since that distance equals the edge length, you get a = 2R. The other expressions would correspond to different contact directions or geometries (for example, touching along a body diagonal or implying an impossible edge size), so they don’t describe the simple cubic packing.

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