Tungsten has a body-centered cubic unit cell and an atomic radius of 141 pm. What is the density

step 1 So the body diagonal length is equal to 4 multiplied with atomic radius, 4 multiplied with 141 p

Tungsten has a body-centered cubic unit cell and an atomic...

Key Concepts

Body-Centered Cubic (BCC) Structure

In crystallography, the body-centered cubic structure is one of the common ways that atoms can be arranged in a crystalline solid. In a BCC unit cell, there is one atom at each of the eight corners of a cube and one atom in the center, creating a total of two atoms per unit cell. Understanding the BCC arrangement is key to determining how atoms pack together and how many atoms are contained within a given volume, which, in turn, is essential for density calculations.

Unit Cell Geometry and Atomic Radius

The atomic radius is the distance from the center of an atom to its outer boundary, and it plays a critical role in defining the size of a unit cell. For a body-centered cubic structure, there is a specific geometric relationship between the atomic radius and the edge length of the cube, typically given by the formula a = (4r)/?3. This relationship allows the conversion of atomic dimensions into the dimensions of the unit cell, enabling calculations of the cell's volume.

Density Calculation

Density is a fundamental physical property defined as mass per unit volume. In the context of a crystalline solid, the mass of a unit cell is determined by multiplying the number of atoms in the cell by the mass of a single atom. The volume of the unit cell can be derived from its edge length. Consequently, calculating the density involves dividing the total mass of the atoms within the unit cell by the volume of the cell.

Avogadro's Number and Molar Mass

Avogadro's number, which is approximately 6.022 × 10^23 atoms per mole, serves as the bridge between microscopic atomic masses and macroscopic mass measurements. By using the molar mass of an element (mass per mole of atoms) and Avogadro's number, one can determine the mass of a single atom. This conversion is critical in the process of calculating the mass contained within a unit cell, and hence for determining the density of the material.

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