College Physics (4th Edition)

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

Chapter 27 - Problems - Page 1042: 28


The frequency of the scattered photon is $2.4\times 10^{19}~Hz$

Work Step by Step

We can find the initial wavelength: $\lambda_i = \frac{c}{f_i}$ $\lambda_i = \frac{3.0\times 10^8~m/s}{3.0\times 10^{19}~Hz}$ $\lambda_i = 1.00\times 10^{-11}~m$ $\lambda_i = 10.0~pm$ We can find the Compton shift in wavelength: $\Delta \lambda = \frac{h}{mc}~(1-cos~\theta)$ $\Delta \lambda = \frac{6.626\times 10^{-34}~J~s}{(9.1\times 10^{-31}~kg)(3.0\times 10^8~m/s)}~(1-cos~90^{\circ})$ $\Delta \lambda = (2.427~pm)~(1)$ $\Delta \lambda = 2.427~pm$ We can find the wavelength of the scattered photon: $\Delta \lambda = \lambda_f-\lambda_i$ $\lambda_f = \lambda_i+\Delta \lambda$ $\lambda_f = (10.0~pm)+ (2.427~pm)$ $\lambda_f = 12.427~pm$ We can find the frequency of the scattered photon: $f_f = \frac{c}{\lambda_f}$ $f_f = \frac{3.0\times 10^8~m/s}{12.427\times 10^{-12}~m}$ $f_f = 2.4\times 10^{19}~Hz$ The frequency of the scattered photon is $2.4\times 10^{19}~Hz$
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