An accelerated electron behaves as a wave. Its de Broglie wavelength is set by the accelerating voltage V:
λ = h / √(2·m·e·V)
h = 6.626×10⁻³⁴ J·s (Planck constant)
m = 9.109×10⁻³¹ kg (electron mass)
e = 1.602×10⁻¹⁹ C (electron charge)
At 20 kV, λ ≈ 8.7 pm — about 60,000× shorter than visible light (~550 nm). Since the diffraction-limited resolution of any imaging system scales with wavelength (d ≈ 0.61·λ / NA), a shorter λ resolves finer detail: this is why an electron microscope reaches nanometre and sub-nanometre resolution while a light microscope is capped near ~200 nm by the diffraction limit of visible light, no matter how good its lenses are.
- Accelerating voltage — raises electron kinetic energy, shrinking λ and the focal spot size on the sample; the image sharpens as voltage increases.
- SEM — a focused beam rasters across the sample surface; the detector reads back-scattered/secondary electrons to build a topography image.
- TEM — a broad beam illuminates the whole (ultra-thin) sample at once; the detector reads electrons transmitted straight through it, mapping internal density.
- Compare with light microscope — shows the same nanostructure imaged with a fixed ~550 nm visible-light wavelength, capped at the diffraction limit regardless of the electron voltage setting.