The unit cell of nickel arsenide is shown here. (b) What is the empirical formula?

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Identify the types of atoms present in the unit cell. In this case, the blue spheres represent nickel (Ni) atoms and the orange spheres represent arsenic (As) atoms.

Count the number of each type of atom within the unit cell. Note that atoms on the corners, edges, and faces are shared with adjacent unit cells.

Determine the contribution of each atom to the unit cell. Corner atoms contribute 1/8, edge atoms contribute 1/4, face atoms contribute 1/2, and atoms entirely within the cell contribute 1.

Calculate the total number of nickel (Ni) atoms in the unit cell by summing the contributions of all Ni atoms.

Calculate the total number of arsenic (As) atoms in the unit cell by summing the contributions of all As atoms.

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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, ions, or molecules in three-dimensional space. Understanding the dimensions and contents of the unit cell is crucial for determining the empirical formula of a compound, as it provides insight into the ratio of different types of atoms present.

Empirical Formula

The empirical formula represents the simplest whole-number ratio of the elements in a compound. It is derived from the composition of the unit cell, indicating how many atoms of each element are present in the smallest repeating unit. For compounds like nickel arsenide, determining the empirical formula involves analyzing the number of nickel and arsenic atoms within the unit cell.

Coordination Number

The coordination number is the number of nearest neighboring atoms surrounding a central atom in a crystal structure. It is essential for understanding the geometry and stability of the crystal lattice. In the case of nickel arsenide, knowing the coordination number helps in identifying how the nickel and arsenic atoms are arranged and how they interact within the unit cell, which is vital for calculating the empirical formula.

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Coordination Numbers

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What is the minimum number of atoms that could be contained in the unit cell of an element with a face-centered cubic lattice? (a) 1, (b) 2, (c) 3, (d) 4, (e) 5.

Textbook Question

The unit cell of a compound containing potassium, aluminum, and fluorine is shown here. (a) What type of lattice does this crystal possess (all three lattice vectors are mutually perpendicular)?

Textbook Question

Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (a) Which structure(s) corresponds to the densest packing of atoms?