An element crystallizes in a face-centered cubic lattice....

An element crystallizes in a face-centered cubic lattice. The edge of the unit cell is 4.078$\hat{A}$ , and the density of the crystal is 19.30 $\mathrm{g} / \mathrm{cm}^{3} .$ Calculate the atomic weight of the element and identify the element.

Key Concepts

Face-Centered Cubic Lattice

A face-centered cubic (FCC) lattice is a type of crystalline structure where atoms are positioned at each of the cube's corners and the centers of all its faces. This arrangement yields a specific effective number of atoms per unit cell, which is essential for determining properties such as density and atomic weight.

Unit Cell and Its Dimensions

The unit cell is the fundamental repeating building block of a crystal lattice. Its dimensions, especially the edge length in cubic cells, allow for the calculation of the cell's volume, which is critical when relating macroscopic properties like density to the microscopic attributes of the material.

Density Calculation in Crystallography

Density in crystallography is defined as the mass of all atoms in a unit cell divided by the volume of the cell. This concept is used to connect an observable physical property (density) with atomic-scale details such as the number of atoms per unit cell and their individual masses.

Atomic Weight (Molar Mass) Determination

Atomic weight, or molar mass, represents the mass of one mole of atoms of an element. In the context of crystallography, it can be calculated using the relationship between density, unit cell volume, and the number of atoms per unit cell, with Avogadro's number providing the linkage between atomic mass and molar mass.

Avogadro's Number

Avogadro's number is a fundamental constant that defines the number of atoms or molecules in one mole of a substance. It is crucial for converting between the microscopic scale (individual atoms) and the macroscopic scale (molar mass), enabling calculations that relate the atomic structure of materials to their bulk properties.

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