The edge length of the unit cell if the atomic radius of potassium in a body-centered cubic unit cell is 227 pm is to be determined. Concept introduction: Crystal structure or lattice is the three-dimensional representation of atoms and molecules arranged in a particular manner. The unit cell is the smallest part of the lattice that is repeated in all directions to yield the crystal lattice. There are 3 types of cubic unit cells as follows: 1. The simple cubic unit cell 2. Body-centered unit cell 3. Face-centered unit cell In the cubic unit cell, atom at the corner is shared by 8 adjacent cells so the contribution of an atom at the corner is 1 8 , atom at the face is shared by 2 adjacent cells so the contribution of an atom at the face is 1 2 and atom at the body center is shared by 1 cell so the contribution of an atom at the body center is 1 . The number of atoms present in a simple cubic, a body-centered cubic, and a face-centered cubic unit cell are 1, 2 and 4 respectively.

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Chapter 12, Problem 12.92P

Interpretation Introduction

Interpretation:

The edge length of the unit cell if the atomic radius of potassium in a body-centered cubic unit cell is 227 pm is to be determined.

Concept introduction:

Crystal structure or lattice is the three-dimensional representation of atoms and molecules arranged in a particular manner. The unit cell is the smallest part of the lattice that is repeated in all directions to yield the crystal lattice. There are 3 types of cubic unit cells as follows:

1. The simple cubic unit cell

2. Body-centered unit cell

3. Face-centered unit cell

In the cubic unit cell, atom at the corner is shared by 8 adjacent cells so the contribution of an atom at the corner is 18, atom at the face is shared by 2 adjacent cells so the contribution of an atom at the face is 12 and atom at the body center is shared by 1 cell so the contribution of an atom at the body center is 1. The number of atoms present in a simple cubic, a body-centered cubic, and a face-centered cubic unit cell are 1, 2 and 4 respectively.

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