Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (a) Which structure(s) corresponds to the densest packing of atoms?

검증된 단계별 안내

Identify the type of unit cell for each structure: A, B, and C.

Determine the number of atoms per unit cell for each structure.

Calculate the packing efficiency for each type of unit cell.

Compare the packing efficiencies to determine which structure(s) have the densest packing.

Conclude which structure(s) correspond to the densest packing of atoms based on the highest packing efficiency.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Unit Cell

A unit cell is the smallest repeating unit of a crystal lattice that reflects the overall symmetry and structure of the entire crystal. It defines the arrangement of atoms in a solid and can vary in shape, such as cubic, tetragonal, or hexagonal. Understanding unit cells is crucial for analyzing the packing efficiency and density of different crystalline structures.

Atomic Packing Efficiency

Atomic packing efficiency (APE) refers to the fraction of volume in a crystal structure that is occupied by atoms. It is calculated by comparing the volume occupied by the atoms to the total volume of the unit cell. Higher packing efficiency indicates a denser arrangement of atoms, which is important for understanding the physical properties of metals and their stability.

Close-Packed Structures

Close-packed structures, such as face-centered cubic (FCC) and hexagonal close-packed (HCP), are arrangements where atoms are packed together as closely as possible. These structures maximize atomic density and are characterized by specific coordination numbers and packing efficiencies. Identifying these structures is essential for determining which metallic arrangements provide the densest packing.