Silver crystallizes in a face-centered cubic unit cell. Each...

Name: Problem 49, Chapter 13: Chemistry and Chemical Reactivity
Uploaded: 2020-06-11T18:23:38-08:00
Duration: 1 min 44 s
Channel: Catherine Lemar
Description: Silver crystallizes in a face-centered cubic unit cell. Each side of the unit cell has a length of 409 pm. What is the radius of a silver atom? (Hint: Assume the atoms just touch each other on the diagonal across the face of the unit cell. That is, each face atom is touching the four corner atoms.)

Silver crystallizes in a face-centered cubic unit cell. Each side of the unit cell has a length of 409 pm. What is the radius of a silver atom? (Hint: Assume the atoms just touch each other on the diagonal across the face of the unit cell. That is, each face atom is touching the four corner atoms.)

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Key Concepts

Unit Cell

A unit cell is the smallest repeating structure in a crystal lattice that, when repeated in all directions, forms the complete crystal. In an FCC lattice, the unit cell not only defines the overall geometry of the arrangement but also the relationships between the atomic radii and the dimensions of the cell.

Geometric Relationship in FCC Structures

In FCC structures, the atoms touch each other along the face diagonal of the cube. By analyzing the face diagonal, one can derive the relationship between the unit cell side length and the atomic radius. The face diagonal in an FCC cell equals four times the atomic radius, which is key to solving problems that relate unit cell dimensions to atomic size.

Face-Centered Cubic (FCC) Crystal Structure

The FCC structure is a type of crystal lattice wherein atoms are located at each of the cube’s eight corners and at the center of each of its six faces. This arrangement leads to a highly efficient packing of atoms, making it common among many metals, including silver.

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