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 - 12-5 The Solid State: Other Types of Solid Materials - Case Study - Questions - Page 458: 1


240.76 pm

Work Step by Step

The hexagon has all internal angles of $120^{\circ}$ and sides of length 139 pm. Labeling the vertexes from 1 to 6 in a counterclockwise manner starting at the top, we want to know the length of the line connecting 2 to 6. Projecting 1 into this line we get a point 1$^*$ defining the right triangle $1-2-1^*$, where the angle $\widehat{2-1-1^*}$ is $60^{\circ}$ (half of the internal angle). So the length of 2-1$^*$ is given by: $sin\ 60^{\circ}=\sqrt 3/2=\overline{2-1^*}/139\ pm$ $\overline{2-1^*}=120.38\ pm$, which is half of the length we want, so the answer is 240.76 pm
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