(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The distance between crystal planes in a KCl crystal is about [itex]3.14 \times 10 ^{-10}m[/itex]. Calculate the Bragg's reflexion angle of first order for electrons with kinetic energy of 4keV. Compare it with photons that have the same energy.

2. Relevant equations

[itex]\lambda n =2d \sin \theta[/itex].

For an electron, [itex]E _K =(\gamma -1 ) m_e c^2[/itex].

[itex]\lambda _B =\frac{h}{p}[/itex] where [itex]p=\gamma m_e v[/itex].

For photons, [itex]E=\frac{hc}{\lambda}[/itex].

3. The attempt at a solution

Using the equations above and after some algebra, I calculated the velocity of the electrons to be [itex]21530815.57 \frac{m}{s}[/itex], somehow comparable to c.

In the end I found out that for electrons, [itex]\sin \theta \approx 0.053378361[/itex]. I am not sure if theta is in degree or radian. I considered degrees so this gave me about [itex]3.059809004°[/itex].

I've done the same for photons (I noticed that they are X-rays since their wavelength is of the order of the Angstrom). I reached [itex]\theta =29.59784517°[/itex].

I'd like to understand why the results are different and why are the electrons less deviated by the atoms in the crystal than the photons with the same energy.

I guess the mass, the charge and the spin play a role, but I'd like to know which one is greater, etc.

If you have any comment(s) on this, please do it. I'm eager to learn.

Thank you.

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# Homework Help: Physical meaning of a result in Bragg's diffraction

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