Chemistry: The Molecular Nature of Matter and Change 7th Edition

Published by McGraw-Hill Education
ISBN 10: 007351117X
ISBN 13: 978-0-07351-117-7

Chapter 12 - Problems: 12.105

Answer

127.7pm

Work Step by Step

Cubic closest packed structure has packing density of [2] d = π/(3∙√2) ≈ 0.74 One mole atoms is occupy a volume of (M/ρ)∙d and a single atom in closed packed structure occupies V = M∙d/(ρ∙Na) = π∙M/(3∙√2∙ρ∙Na) (Na is the Avogadro constant) Since the atoms ar considered as solid spheres of radius r: (4/3)∙π∙r³ = π∙M/(3∙√2∙ρ∙Na) => r = ∛[ M/(4∙√2∙ρ∙Na) ] = ∛[ 63.55g/mol / (4∙√2 ∙ 8.95d/cm³ ∙ 6.022×10²³mol⁻¹) ] = 1.277×10⁻⁸ cm = 1.277×10⁻¹⁰ m = 127.7pm
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