Concept:This addresses the fundamental scale of quantum mechanical matter waves for particles accelerated to practical laboratory energies.
Formula:$$ \lambda = \frac{h}{\sqrt{2meV}} $$
Solution:- An electron accelerated through typically encountered potentials (tens to thousands of volts) achieves a de Broglie wavelength in the realm of \( 0.01 \text{ nm} \) to \( 1 \text{ nm} \).
- This exact spatial dimension matches the wavelength of X-rays, making crystalline atomic structures excellent diffraction gratings for both X-rays and electrons.
Why other options are incorrect:Visible, Infrared, and Radio waves represent macroscopic wavelengths (hundreds of nanometers to meters) that a high-speed fundamental particle does not naturally mimic.
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