Determine the number of atoms per unit cell for each metal.
(a) Polonium

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Polonium crystallizes in a simple cubic structure.

In a simple cubic unit cell, there is one atom at each corner of the cube.

Each corner atom is shared by eight adjacent unit cells.

Therefore, each corner contributes \( \frac{1}{8} \) of an atom to the unit cell.

Since there are 8 corners, the total number of atoms per unit cell is \( 8 \times \frac{1}{8} = 1 \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Unit Cell

A unit cell is the smallest repeating unit in a crystal lattice that reflects the symmetry and structure of the entire crystal. It defines the arrangement of atoms in a solid and is characterized by its dimensions and angles. Understanding the unit cell is crucial for determining the number of atoms it contains, which can vary based on the type of crystal structure.

Atomic Packing Factor (APF)

The Atomic Packing Factor (APF) is a measure of how efficiently atoms are packed in a unit cell. It is calculated as the volume occupied by the atoms in the unit cell divided by the total volume of the unit cell. Different metals have different APFs depending on their crystal structures, which influences their physical properties and the number of atoms per unit cell.

Crystal Structure

Crystal structure refers to the ordered arrangement of atoms in a crystalline material. Metals can adopt various crystal structures, such as face-centered cubic (FCC), body-centered cubic (BCC), or hexagonal close-packed (HCP). The specific structure of a metal like polonium will determine how many atoms are present in its unit cell, which is essential for understanding its properties and behavior.

Determine the number of atoms per unit cell for each metal.(a) Polonium