Chemistry and Chemical Reactivity (9th Edition)

Published by Cengage Learning
ISBN 10: 1133949649
ISBN 13: 978-1-13394-964-0

Chapter 12 The Solid State - Study Questions - Page 467a: 7


197 pm

Work Step by Step

For a face-centered cubic arrangement there are $8 \times 1/8$ atoms in the corners and $6\times1/2$ in the faces, so 4 atoms per unit cell: Mass: $4\times 40.078\ g/mol\div 6.022\times 10^{23}\ atoms/mol=2.662\times10^{-22}\ g/cell$ Volume: $2.662\times10^{-22}\ g/cell\div 1.54\ g/cm^3=1.729\times 10^{-22}\ cm^3/cell$ Side length: $\sqrt[3]{1.729\times 10^{-22}\ cm^3}=5.57\times10^{-8}\ cm=557\ pm$ The diagonal of a side equals the radius of two atoms in the vertexes plus the diameter of the one in the face, so: $557\ pm\times \sqrt2 =4.r\rightarrow r=197\ pm$
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