Question #268417

X-ray with energy 12 keV is used to measure Bragg-reflection peaks. The third-order peak is measured for the X-ray beam incident at an angle of 30 degrees with

respect to the horizontal. What is the spacing between the atomic planes? What

is the angle at which the first-order reflection peak is observed?


1
Expert's answer
2021-11-19T10:51:32-0500

2dsinα=nλ2d\sin\alpha=n\lambda


hν=hc/λ=Eλ=hc/E=h\nu=hc/\lambda=E\to \lambda=hc/E=


=6.62610243108/(120001.61019)==6.626\cdot10^{-24}\cdot3\cdot10^8/(12000\cdot1.6\cdot10^{-19})=


=1.0351010 (m).=1.035\cdot10^{-10}\ (m).


a. 2dsin30°=31.0351010d=3.11010 (m)2d\sin30°=3\cdot1.035\cdot10^{-10}\to d=3.1\cdot10^{-10}\ (m)


b. 23.11010sinα=11.03510102\cdot3.1\cdot10^{-10}\cdot\sin\alpha=1\cdot1.035\cdot10^{-10}\to


α=9.6°\alpha=9.6°


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