The density of silver is 10.50 g ·cm^-3 at 20^∘ C. Given that the unit cell of silver is face-c

step 1 In this question, we wanted to determine the length given a first centred cubic unit cell. So lo

The density of silver is 10.50 g ·cm^-3 at 20^∘ C. Given...

The density of silver is $10.50 \mathrm{~g} \cdot \mathrm{cm}^{-3}$ at $20^{\circ} \mathrm{C}$. Given that the unit cell of silver is face-centered cubic, calculate the length of an edge of a unit cell.

Key Concepts

Density

Density is a fundamental material property defined as mass per unit volume. It is used to relate the amount of matter contained in a given volume, which is essential when connecting microscopic unit cell dimensions with macroscopic properties of a material.

Unit Cell

A unit cell is the smallest repeating structural unit in a crystal lattice that, when repeated in three dimensions, composes the entire crystal. Its geometry and contents determine many physical properties of the material.

Face-Centered Cubic (FCC) Crystal Structure

The face-centered cubic (FCC) structure is a type of crystal arrangement where atoms occupy each of the cube's corners and the centers of each face. This configuration results in a specific number of atoms per unit cell (effectively 4) and characteristic spatial relationships used in determining lattice parameters.

Avogadro's Number and Molar Mass

Avogadro's number connects the macroscopic scale to the atomic scale by defining the number of atoms in one mole of a substance. By combining this constant with the molar mass, one can calculate the mass of a single atom and thereby relate atomic-level information to bulk properties like density.

Determination of Unit Cell Edge Length

By relating the total mass of the atoms within a unit cell (using the number of atoms per cell and the mass of each atom) to the density of the material, one can derive the unit cell volume. From the volume of the cubic cell, the edge length is obtained by taking the cube root. This process ties together the microscopic atomic arrangement with the observable structure dimensions.

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