You use x-ray photons of wavelength 0.251 nm in a Compton-scattering experiment. At a scattering angle of 14.5 ∘ , what is the increase in the wavelength of the scattered x rays compared to the incident x rays? Express your results in nm.

Question

You use x-ray photons of wavelength 0.251 nm in a Compton-scattering experiment. At a scattering angle of       14.5    ∘  , what is the increase in the wavelength of the scattered x rays compared to the incident x rays? Express your results in nm.

Frances Dodson · Accepted Answer

We have the expression of the Compton effect,      λ    f    −      λ    i    =      h                  m        e            c        (  1  −  cos  ⁡  θ  )So, we easily calculate the final wavelength,      λ    f    −  0.251  ×      10          −      9        =            6.626      ×              10                  −          34                            9.1      ×              10                  −          31                    ×      3      ×              10        8              (  1  −  cos  ⁡  (      14.5    ∘    )  )        λ    f    −  0.251  ×      10          −      9        =            6.626      ×              10                  −          34                            27.3      ×              10                  −          23                      (  1  −  0.9681  )        λ    f    −  0.251  ×      10          −      9        =  0.2427  ×      10          −      11        ×  0.0319    0.251  ×      10          −      9        =  0.0077  ×      10          −      11              λ    f    =  0.251077  ×      10          −      9           mSo, the increasing wavelength,  △  λ  =      λ    f    −      λ    i      △  λ  =  0.000077  ×      10          −      9           mBut we have to calculate in nmso, we change m into nm  △  λ  =  0.000077     n  m

You use x-ray photons of wavelength 0.251 nm in a Compton-scattering experiment. At a scattering angle of 14.5°, what is the increase in the wavelength of the scattered x rays compared to the incident x rays?

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