## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 27 - Problems - Page 1042: 22

#### Answer

(a) $\lambda = 10.71~pm$ (b) $\lambda = 12.43~pm$

#### Work Step by Step

(a) We can find the wavelengths of the scattered x-rays: $\lambda_f = \lambda_i+ \frac{h}{mc}~(1-cos~\theta)$ $\lambda_f = (10.0~pm)+ \frac{6.626\times 10^{-34}~J~s}{(9.1\times 10^{-31}~kg)(3.0\times 10^8~m/s)}~(1-cos~45.0^{\circ})$ $\lambda_f = (10.0~pm)+ (2.427~pm)~(1-cos~45.0^{\circ})$ $\lambda = 10.71~pm$ (b) We can find the wavelengths of the scattered x-rays: $\lambda_f = \lambda_i+ \frac{h}{mc}~(1-cos~\theta)$ $\lambda_f = (10.0~pm)+ \frac{6.626\times 10^{-34}~J~s}{(9.1\times 10^{-31}~kg)(3.0\times 10^8~m/s)}~(1-cos~90.0^{\circ})$ $\lambda_f = (10.0~pm)+ (2.427~pm)~(1)$ $\lambda = 12.43~pm$

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