A Group 4A element with a density of 11.35 g / cm^3 crystallizes in a face-centered cubic latti

step 1 Here we are continuing on with unit cells. And so the first thing we need to do is calculate the

A Group 4A element with a density of 11.35 g / cm^3...

A Group 4A element with a density of $11.35 \mathrm{~g} / \mathrm{cm}^{3}$ crystallizes in a face-centered cubic lattice whose unit cell edge length is $4.95 \AA$. Calculate its atomic weight. What is the element?

Key Concepts

Face-Centered Cubic (FCC) Lattice

The FCC lattice is one of the common crystal structures where atoms are located at each of the cube's corners as well as at the centers of each face. This arrangement results in a specific number of atoms per unit cell (typically 4) and has distinct geometrical and packing characteristics that are essential for relating the structure to physical properties such as density.

Unit Cell Dimensions and Volume

The unit cell is the smallest repeating unit in a crystal lattice that, when repeated in space, constitutes the entire lattice. Its edge length is used to calculate the cell’s volume, which is a critical step in determining properties such as density and mass per unit cell.

Density and Mass Relationships in Crystals

The density of a crystalline material can be expressed as the mass of atoms contained within a unit cell divided by the volume of that cell. This relationship is a fundamental concept in solid-state chemistry and physics, linking microscopic atomic structure to macroscopic physical properties.

Atomic Weight Determination

By combining the known density, the unit cell dimensions, and the number of atoms per unit cell (derived from the lattice structure), one can calculate the atomic weight of the element. This method uses the relationship between the molar mass, Avogadro's number, and the computed mass of the atoms within a unit cell to determine the element’s atomic weight.

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