Fundamentals of Materials Science and Engineering, Binder Ready Version: An Integrated Approach
5th Edition
ISBN: 9781119175483
Author: William D. Callister Jr., David G. Rethwisch
Publisher: WILEY
Question
Chapter 5.13, Problem 1QP
To determine

## The total number of lattice site in sliver (Ag) at 700∘C .

The total number of lattice site in sliver (Ag) at 700C is 1.156×1023vacancies/m3_ .

### Explanation of Solution

Given:

The atomic weight of silver, AAg=107.87g/mol .

The theoretical density of silver, ρAg=10.35g/cm3 .

The absolute temperature of sliver is 700C .

The number of vacancies per unit volume, Nν=2×106 .

Explanation:

Write the expression of atomic site per cubic meter.

NAg=NAρAgAAg (I)

Here, Avogadro’s number (6.022×1023atoms/mol) is NA .

Write the expression of vacancies per meter cubic.

Nν=(2×106)NAg (II)

Conclusion:

Substitute 107.87g/mol for AAg , 10.35g/cm3 for ρAg , and (6.022×1023atoms/mol) for NA in Equation (I).

NAg=(6.022×1023atoms/mol)(10.35g/cm3)(106cm3/m3)(107.87g/mol)=(6.23277×1024)(106cm3/m3)(107.87g/mol)=5.78×1028atoms/m3

Substitute 5.78×1028atoms/m3 for NAg in Equation (II).

Nν=(2×106)(5.78×1028atoms/m3)=1.156×1023vacancies/m3

Thus, the total number of lattice site in sliver (Ag) at 700C is 1.156×1023vacancies/m3_ .

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