Hi - come across a problem I am unsure if I am doing the right way.(adsbygoogle = window.adsbygoogle || []).push({});

At what energy is Bragg's Law satisfied to first order in Cu given that the lattice parameter is a=0.361nm

i) Electrons propogate in the [100] direction

ii) [110] direction

My basic step was

[tex]$2d_{hkl} \sin \theta = n\lambda $

[/tex]

[tex]$d_{hkl} = \frac{a}{{\sqrt {h^2 + k^2 + l^2 } }}$

[/tex]

I was unsure what to do with theta, however I seem to recall coming across a similar problem, where we assumed electon-lattic interctions caused a reflection, so theta=90. However this seems a little hazy to me.

So upon finding the wavelength I then used

[tex]$E = \frac{{\hbar ^2 }}{{2m}}\left| k \right|^2 {\rm{, where }}k = \frac{{2\pi }}{\lambda }$

[/tex]

I think I got about 2 ev. Is this the right approach?

And finally...comparing this to the Fermi energy of Cu (7ev), "comment on the significant of this comparision with respect to teh assumption of free electrons in Cu". Since E < E[f], do I conclude this is a good assumption??

Thanks in advance

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# Electrons & Braggs Law

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