Solved: If a photon of wavelength 0.04250 nm strikes a

Chapter 38, Problem 21E

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QUESTION:

Problem 21E

If a photon of wavelength 0.04250 nm strikes a free electron and is scattered at an angle of 35.0° from its original direction, find (a) the change in the wavelength of this photon; (b) the wavelength of the scattered light; (c) the change in energy of the photon (is it a loss or a gain?); (d) the energy gained by the electron.

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Questions & Answers

QUESTION:

Problem 21E

ANSWER:

Step 1 of 4

$When\ photon\ of\ wavelength\ 0.04250\ nm\ strikes\ a\ free\ electron\ and\ is\ scattered\ at\ an\ angle\ of$

$\ 35.0°\ from\ its\ original\ direction\ then\ we\ have\ to\ find\ the\ change\ in\ wavelength\ of\ ,\ scattered$

$\ wavelength\ and\ energy\ of\ the\ photon.$

$The\ shift\ in\ wavelength\ of\ the\ photon\ is$

$\lambda{}'-\lambda{}=\frac{h}{mc}(1-cos\varphi{})$ $\ where\ λ′\ is\ the\ wavelength\ after\ the\ scattering\ and\ \frac{h}{mc}={\lambda{}}_{c}=2.426\times{}{10}^{-12}m$ $The\ energy\ of\ the\ photon\ of\ wavelength\ \lambda{}\ is,\$

$E=\frac{hc}{\lambda{}}=\frac{1.24\times{}{10}^{-6}eV.m}{\lambda{}}$ $Conservation\ of\ energy\ applies\ to\ the\ collision,\ so\ the\ energy\ lost\ by\ the\ photon\ equals\ the\ energy\$ $\ gained\ by\ the\ electron.\$