Explanation 1) Concept: We have to first find initial energy from the given wavelength. Then find new wavelength, and from the new wavelength, we can find new energy. Using this energy, we can find kinetic energy. 2) Formula: i) E = h c λ ii) ∆ λ = h m c ( 1 - c o s ϕ ) 3) Given: i) Initial wavelength is 3 × 10 - 12 m ii) Angle ϕ = 90 ° 4) Calculations: The initial wavelength is λ = 3.00 × 10 - 12 m So initial energy is as follows: E = h c λ E = 1240 e V n m 0.003 n m Here, we have used h c = 1240 e V n m ∴ E = 4.13 × 10 5 e V Now Compton shift is as follows: ∆ λ = h m c ( 1 - c o s ϕ ) ∆ λ = h m c ( 1 - cos ⁡ 90 ) ∆ λ = h c m c 2 Substituting the values, we get ∆ λ = 1240 e V n m 511 × 10 3 e V ∆ λ = 2

Fundamentals of Physics, Volume 1, Chapter 1-20

10th Edition

ISBN: 9781118233764

Author: David Halliday

Publisher: WILEY

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Chapter 38, Problem 34P

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Electron’s kinetic energy.

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A photon undergoes Compton scattering off a stationary free electron. The photon scatters at 90.0° from its initial direction; its initial wavelength is 3.00*10-12 m. What is the electron’s kinetic energy?

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Problem 4: A photon originally traveling along the x axis, with wavelength λ = 0.100 nm is incident on an electron (m = 9.109 x 10-31 kg) that is initially at rest. The x-component of the momentum of the electron after the collision is 5.0 x 10-24 kg m/s and the y-component of the momentum of the electron after the collision is -6.0 x 10-24 kg m/s. If the photon scatters at an angle + from its original direction, what is wavelength of the photon after the collision. h= 6.626 x 10:34 J·s and c = 3.0 x 108 m/s.

Chapter 38 Solutions

Fundamentals of Physics, Volume 1, Chapter 1-20

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Chapter 38 Solutions

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Electron’s kinetic energy.