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**1. Homework Statement**

A photon scatters in the backward direction ([tex]\theta[/tex]= 180) from a free proton that is initially at rest.

What must the wavelength of the incident photon be if it is to undergo a 10.0% change in wavelength as a result of the scattering?

**2. Homework Equations**

[tex]\lambda[/tex]'-[tex]\lambda[/tex] = (h/mc)(1-cos([tex]\theta[/tex]))

where the left side is the difference between scattered and incidence wavelengths.

**3. The Attempt at a Solution**

This seemed like a pretty straightforward problem. Since the photon undergoes a 10% change in wavelength, 1.1[tex]\lambda[/tex] = [tex]\lambda[/tex]'. Therefore .1[tex]\lambda[/tex] = (h/mc)(1-cos([tex]\theta[/tex])). Multiply by 10 and evaluate the cosine, and you get [tex]\lambda[/tex] = 20h/mc. However, when I substitute values into this and evaluate it I get the wrong answer. I have absolutely no clue what I am doing wrong here. This shouldn't be a difficult problem, but for some reason I am not getting the correct answer. Help would be appreciated. Thanks.