Calculating Bragg Angles for X-Ray Scattering from Table Salt Crystal

  • #1
transmini
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Homework Statement


The Spacing between the Na and Cl atoms in table salt (NaCl) is ##d=2.82x10^{-10}m##, which was first deduced from Bragg scattering. For an experiment where X-rays of energy 20 eV are produced, what are the corresponding Bragg angles below ##90^{\circ}## for scattering from a large crystal of table salt?

Homework Equations


Bragg's Law: ##2dsin(\theta)=n\lambda##

The Attempt at a Solution


##sin(\theta)=\frac{n\lambda}{2d}##
##\lambda = \frac{hc}{E_{photon}}##
##\theta = sin^{-1}(\frac{nhc}{2dE})##
##\theta = sin^{-1}(\frac{n*1240eV\dot nm}{2*0.282nm*20eV})##
##\theta = sin^{-1}(n*109)##

but this isn't within the domain of arcsin. So are there just no Bragg's angles here? Or is there a different energy that I'm using rather than 20 eV?
 
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  • #2
I believe your calculations are correct. Perhaps someone else can also check the numbers, but I think the x-ray energies need to be more like 20 keV.
 
  • #3
Definitely in the keV region. From memory, Cu Kα, a common source, is around 8 keV.
 
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  • #4
After turning in the work today, the professor mentioned there was a typo in the book and he failed to email us to tell us that before hand. It was in fact supposed to be 20 keV.
 
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