Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 18 - A Macroscopic Description of Matter - Exercises and Problems: 41

Answer

The smallest distance between two copper atoms is $2.29\times 10^{-10}~m$

Work Step by Step

Let's assume that we have 1 mole of copper atoms. We can find the mass. $m = (6.02\times 10^{23})(64)(1.66\times 10^{-27}~kg)$ $m = 0.06396~kg$ We can find the volume of the copper cube. $V = \frac{m}{\rho}$ $V = \frac{0.06396~kg}{8.9\times 10^3~kg/m^3}$ $V = 7.187\times 10^{-6}~m^3$ We can find the length $L$ of each side of the cube. $L = V^{1/3}$ $L = (7.187\times 10^{-6}~m^3)^{1/3}$ $L = 0.0193~m$ We can find the number of atoms along each side of the cube. $(6.02\times 10^{23})^{1/3} = 8.44\times 10^7~atoms$ We can find the distance $d$ between the atoms along the side of the cube. $d = \frac{0.0193~m}{8.44\times 10^7}$ $d = 2.29\times 10^{-10}~m$ The smallest distance between two copper atoms is $2.29\times 10^{-10}~m$.
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