   Chapter 21, Problem 122SCQ

Chapter
Section
Textbook Problem

The density of lead is 11.350 g/cm3, and the metal crystallizes in a face-centered cubic unit cell. Estimate the radius of a lead atom.

Interpretation Introduction

Interpretation:

To estimate the radius of lead atom.

Concept introduction:

Lead belongs to group 4A of the periodic table. Lead and its compounds are considered poisonous and can cause lead poisoning in individuals. The salts of lead are sweet in taste.

Lead crystallizes in fcc (face centred cubic) unit cell. The density of lead is 11.350 g/cm3. The density is expressed by the formula,

d=Z×Ma3×Na

Where d is the density,Na is the Avogadro number, M is the mass and a is the edge length.

Explanation

The radius of lead atom is calculated below.

Given:

The density of lead is 11.350 g/cm3.

The density is expressed by the formula,

d=Z×Ma3×Na

The rearranged expression is,

a3=Z×Md×Na

For fcc, the value of Z=4

The atomic mass of lead is 207 g mol1.

The value of Na is 6.023×1023mol1.

Substitute the values,

a3=(4)(207 g mol1)(11

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