The X-rays detected at a scattering angle of θ = 158° have a wavelength of 0.1804 nm. Calculate the wavelength of an incident photon.
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Since x-rays undergo Compton scattering, we can use that result here. The formula is:
λ₂ - λ₁ = λ' (1 - cosθ)
Where I have used λ' as the Compton wavelength, equal to 2.43*10^(-12) m. We also have that θ = 158° and λ₂ = 0.1804 nm = 1.804*10^(-10) m so sub those in:
λ₁ = λ₂ - λ' (1 - cosθ)
λ₁ = 0.1804*10^(-9) m - (2.43*10^(-12) m)(1 - cos(158°))
λ₁ = 1.757*10^(-10) m = 0.1757 nm
Done!
λ₂ - λ₁ = λ' (1 - cosθ)
Where I have used λ' as the Compton wavelength, equal to 2.43*10^(-12) m. We also have that θ = 158° and λ₂ = 0.1804 nm = 1.804*10^(-10) m so sub those in:
λ₁ = λ₂ - λ' (1 - cosθ)
λ₁ = 0.1804*10^(-9) m - (2.43*10^(-12) m)(1 - cos(158°))
λ₁ = 1.757*10^(-10) m = 0.1757 nm
Done!