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 - Additional Exercises: 6.81a

Answer

The wavelength of wave A is $\lambda_A=35.56nm$ The wavelength of wave B is $\lambda_B=80nm$

Work Step by Step

The wavelength of a wave is the distance between 2 adjacent peaks (or 2 adjacent troughs) of that wave. *Wave A: We would call the distance between A and the point where the red line passes the black line for the first time by $a$. We can see that $$9a=1.6\times10^{-7}m$$$$a\approx1.778\times10^{-8}m$$ Now we measure the distance between 2 adjacent peaks, which is the wavelength of wave A $(\lambda_A)$. We also find that $$\lambda_A=2a=2\times(1.778\times10^{-8}m)$$$$\lambda_A=3.556\times10^{-8}m=35.56nm$$ *Wave B: Similary, we call the distance between B and the point where the red line passes the black line for the first time by $b$. We can see that $$4b=1.6\times10^{-7}m$$$$b=4\times10^{-8}m$$ Now we measure the distance between 2 adjacent peaks, which is the wavelength of wave B $(\lambda_B)$. We also find that $$\lambda_B=2b=2\times(4\times10^{-8}m)$$$$\lambda_B=8\times10^{-8}m=80nm$$
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