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The greatest observed shift in wavelength, as seen in the scattered photon, when an x-ray photon of wavelength 0. 10 nm is compton-scattered from a free electron is 0.048 nm.
How to find the shift in wavelength?
The shift in wavelength can be find out using the Compton effect formula. It is given as,
[tex]\Delta \lambda=\dfrac{h}{m_oC}(1-\cos \theta)[/tex]
Here, h is the planks constant (6.63 × 10⁻³⁴ J-s), m₀ is the mass of electron (9.1×10⁻³¹ kg), C is the speed of light (3×10⁸ m/s).
An x-ray photon of wavelength 0. 10 nm is compton-scattered from a free electron.
At the value of cos theta in above formula equal to -1, we get the greatest observed shift in wavelength. Thus, put the values,
[tex]\Delta \lambda=\dfrac{6.63\times10^{-34}}{9.1\times10^{-31}\times3\times10^8}}(1-(-1))\\\Delta \lambda=4.857\times10^{-12}\rm \; m\\\Delta \lambda=0.048\rm\; nm[/tex]
Thus, the greatest observed shift in wavelength, as seen in the scattered photon, when an x-ray photon of wavelength 0. 10 nm is compton-scattered from a free electron is 0.048 nm.
Learn more about the shift in wavelength here;
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