Physics Asked on May 14, 2021
My textbook (Arthur Beiser Intro to Modern Physics) states that "unbound low-energy electrons can travel freely through a crystal since their waves are long relative to the lattice spacing $a$ " in the chapter on solid state physics.
Now I understand that high-energy electrons with wavelengths comparable to the lattice spacing $a$ will undergo diffraction (just like x-rays diffract when they impinge upon a crystal). Hence these electrons will not be able to travel freely through the lattice. Clearly this diffraction will not occur for low-energy electrons with wavelengths much longer than $a$. But surely these low-energy electrons will still reflect off the lattice planes in the same way that visible light reflects off a crystal (as opposed to x-rays which diffract off the lattice)? The fact that the low energy electrons have wavelengths much longer than $a$ doesn’t seem to indicate that they should be able to travel freely through the lattice because they should still be reflecting off the bragg planes. So why does the author infer that low energy electrons should be able to travel freely through the crystal?
Any help on this issue would be most appreciated!
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