   Chapter 22.7, Problem 1.2ACP

Chapter
Section
Textbook Problem

Copper has a face-centered cubic unit cell. If copper has a density of 8.960 g/cm3, what is the radius of a copper atom?

Interpretation Introduction

Interpretation:

The radius of copper atom has to be calculated.

Concept introduction:

• An ionic radii are the radius of an atom's ion in ionic crystals structure.
• An ionic solid is made up cations and anions held together by electrostatic forces in a rigid array or lattice.
• Positive charge ions are cations and negative charge ions are anions.
• Lattice Energy is mainly depends on the charge on the ion and radius or size of the ion.
• Ionic radius increases from top to bottom on the periodic table and ionic radius decreases from left to right the periodic table.
• Determining the volume of the unit cell:

Massdensity = volume

Explanation

The density of the copper atom is given below,

density=8.960g/cm3

Determining the mass of four atoms of Cu in a unit cell

63.546  g6.022 × 1023atoms/mol  = 10.551 × 10¯23g/atom10.551 × 10¯23g/atom  × 4 atoms = 4.220 × 10¯22g

Determining the volume of the unit cell:

Massdensity = volume

4.220 × 10¯22g8.960g/cm3 = volumevolume =4.71×10-23cm3

Determining the edge length of the unit cell:

V= d3

d =(4

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