Zinc has an HCP crystal structure, a c / a ratio of 1.856, and a density of 7.13 g / cm^3. Comp

step 1 As we know that Vc is equal to 6 R square C root 3. So putting the value here I can write the va

Zinc has an HCP crystal structure, a c / a ratio of 1.856,...

Key Concepts

Hexagonal Close-Packed (HCP) Crystal Structure

The HCP structure is one of the common crystal lattices in which atoms occupy positions defined by a hexagonally arranged basal plane and a second plane that fills the interstitial positions. It features a characteristic unit cell with a particular arrangement of atoms that leads to a specific packing efficiency, which is critical for linking structural parameters to physical properties such as density.

Lattice Parameters and the c/a Ratio

The lattice parameters describe the dimensions of the unit cell in crystalline materials, and the c/a ratio is a specific measure of the relative length of the cell along the vertical axis (c) compared to the horizontal base (a). In HCP structures, the c/a ratio is important because it influences the geometry of atomic packing and is essential when calculating distances between atoms, such as the atomic radius, from the unit cell dimensions.

Density of Crystalline Solids

Density in crystalline materials is defined as the mass of the atoms in the unit cell divided by the volume of the cell. By combining the known density with the unit cell dimensions and the number of atoms per cell, one can determine key structural parameters such as the volume per atom, which is crucial for further calculations including the atomic radius.

Atomic Radius Calculation

The atomic radius in a crystalline solid can be computed by relating the unit cell geometry and the number of atoms per cell to the real physical space occupied by an individual atom. This involves using the relationships derived from the lattice parameters and packing considerations, thereby connecting macroscopic properties like density with microscopic dimensions such as the atomic radius.

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