I'm currently reviewing Bragg scattering. The particular problem below has me slightly confused on whether I'm thinking about it correctly.


Is the problem below referring to the kinetic energy of the neutrons when it mentions "energy"? Does the "other energies" of neutrons result from specific neutron wavelengths and diffraction orders $n$?



My Attempt

  • Plane separation $d=0.247\rm\,nm$
  • Kinetic energy of Neutron to select $K=0.0105\rm\,eV$
  • Neutron mass $m_N=939.6\,\mathrm{MeV}/c^2$

Using non-relativistic approximation, kinetic energy is $K=p^2/2m$. Therefore, rearranging this gives


With de Broglie's wavelength formula,

$$\lambda = \frac{h}{p} = \frac{h}{\sqrt{2mK}}$$

Finally, Braggs formula is


With these formulas, I find $\lambda=2.79\times 10^{-10}\,\rm m$ and $\theta = 34.4\deg$ for 4a).

For 4b), I presumed that the other energies must correspond to any wavelength $\frac{\lambda}{q}$, where $q$ is any natural number. Therefore, using the kinetic energy and de Broglie's formula above

$$ K_q=\frac{p^2}{2m}=\frac{(h/\lambda_q)^2}{2m}=\frac{(qh/\lambda)^2}{2m}=q^2K=q^2\,0.0105\, \,\rm eV$$


closed as off-topic by John Rennie, ACuriousMind, Ryan Unger, Danu, yuggib Sep 8 '15 at 21:39

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  • 1
    $\begingroup$ Note that our policy is to not do people's homework for them, including checking their work. This is being flagged as off-topic, and indeed it appears to be a check-my-work problem. But if you really just want answers to what you've labeled "questions" you should be fine. Since we don't really need to see your work to answer those questions, I suggest removing it (but leaving the original problem statement). $\endgroup$ – user10851 Sep 2 '15 at 0:46
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    $\begingroup$ @ChrisWhite, I would like the questions I've asked to be answered. I figured I'd add my attempt to show that I have at least thought about the problem. Perhaps I should move my attempt as an answer? $\endgroup$ – Akyidrian Sep 2 '15 at 1:33

While your answer has elements of "check my work" in it, as discussed in the comments above, I think the basic questions you posed are legitimate.

Yes, the question refers to the kinetic energy of the neutrons, and the de Broglie wavelength associated with them; and yes, "other energies" will appear because higher order scattering can occur between the same planes, resulting in $n\cdot E_0$ energies being present in the diffracted beam.

Note - I did not "check your work". But superficially, it looks like you are on track.


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