Chemistry: The Central Science (13th Edition)

Published by Prentice Hall
ISBN 10: 0321910419
ISBN 13: 978-0-32191-041-7

Chapter 6 - Electronic Structure of Atoms - Exercises: 6.47d

Answer

The wavelength of the ozone molecule is $1.511\times10^{-11}m$.

Work Step by Step

*The de Broglie relationship: $$\lambda=\frac{h}{mv}$$ $\lambda$: wavelength of object $h$: Planck's constant ($h=6.626\times10^{-34} J.s$) $m$: mass of object $v$: velocity of object 1) Find the known variables - Mass of the ozone molecule: The molecular weight of ozone is $48g/mol$. $1 mol$ would have $6.022\times10^{23}$ molecules. So, 1 molecule of ozone would weigh $(48g/mol)\times\frac{1mol}{6.022\times10^{23}molecules}\approx7.971\times10^{-23}g/molecule\approx7.971\times10^{-26}kg/molecule$ In other words, $m=7.971\times10^{-26}kg$ - Velocity of the ozone molecule: $v=550m/s$ 2) Calculate the wavelength of the ozone molecule $\lambda=\frac{h}{mv}=\frac{6.626\times10^{-34}}{(7.971\times10^{-26})\times550}\approx1.511\times10^{-11}m$
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