Chapter 38, Problem 032 X rays of wavelength 0.0179 nm are directed in the posit

Question

Chapter 38, Problem 032 X rays of wavelength 0.0179 nm are directed in the positive direction of an x axis onto a target containing loosely bound electrons. For Compton scattering from one of those electrons, at an angle of 148°, what are (a) the Compton shift, (b) the corresponding change in photon energy, (e) the kinetic energy of the recolling electron, and (d) the angle between the positive direction of the x axis and the electron's direction of motion? The electron Compton wavelength is 2.43 x 1012 m. (a) Number (b) Number (c) Number (d) Number Show Work is REQUIRED for this question: Open Show Work Units l- Units Units Units

Explanation / Answer

lambda = 0.0179*10^-9 m

theta = 148 deg

hence

lambda' - lambda = h(1 - cos(theta))/me*c

a. compton shift = 6.63*10^-34 ( 1- cos(148))/9.1*10^-31 * 3*10^8

compton shift = 4.488*10^-12 m

b. chang ein photon energy = hc(1/lambda - 1/lambda')

lambda = 0.0179*10^-9 m

lambda' = 2.2388*10^-11 m

hence

dE = 2.227*10^-15 J = 13922.2156 eV

c. KE of recoil electron = 13922.2156 eV

d. spee dof electron = v

0.5mv^2 = KE

v = 6.99*10^7 m/s

hence

mvsin(phi) = hsin(theta)/lambda'

phi = 14.26 deg

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