Answer to Question #268417 in Optics for sai

Question

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?

Answer 1

$2d\sin\alpha=n\lambda$

$h\nu=hc/\lambda=E\to \lambda=hc/E=$

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

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

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

b. $2\cdot3.1\cdot10^{-10}\cdot\sin\alpha=1\cdot1.035\cdot10^{-10}\to$

$\alpha=9.6°$