College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 13 - Problems - Page 498: 34


There are $1.76\times 10^{23}$ carbon atoms per $cm^3$

Work Step by Step

A carbon atom consists of 6 protons and 6 neutrons. The mass of one atom of carbon is $12~u$ We can find the mass of one carbon atom: $m = (12~u)(1.66\times 10^{-27}~kg/u) = 1.99\times 10^{-26}~kg$ We can find the mass of carbon per $cm^3$: $m_c = 3500~kg/m^3\times \frac{1~m^3}{10^6~cm^3} = 3.5\times 10^{-3}~kg/cm^3$ We can find the number of carbon atoms per $cm^3$: $\frac{3.5\times 10^{-3}~kg/cm^3}{1.99\times 10^{-26}~kg/atom} = 1.76\times 10^{23}~atoms/cm^3$ There are $1.76\times 10^{23}$ carbon atoms per $cm^3$.
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