   Chapter 12, Problem 9PS

Chapter
Section
Textbook Problem

Calcium metal crystallizes in a face-centered cubic unit cell. The density of the solid is 1.54 g/cm3. What is the radius of a calcium atom?

Interpretation Introduction

Interpretation:

The radius of the calcium atom has to be identified.

Concept introduction:

• 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.
• Ionic radius decreases from left to right the periodic table.

Determining the volume of the unit cell:

Massdensity = volume

Explanation

The density of the calcium atom is given below,

density=1.54g/cm3

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

40.08 g6.022 × 1023atoms/mol  = 6.6556 × 10¯23g/atom

Since the number of atom per unit cell in an FCC structure is 4,

6.6556 × 10¯23g/atom  × 4 atoms = 2.66224 × 10¯22g

Determining the volume of the unit cell:

Massdensity = volume

2.66224 × 10-22g1.54g/cm3 = volumevolume =1.73×10-22cm3

Determining the edge length of the unit cell:

d = 1

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