We’re not too far from the end of the Physics 202 class I’m helping teach, and as we finish things out we’re learning about the particle nature of light and the wave nature of matter. It’s really the very basics of quantum mechanics. One of the applications of this kind of knowledge is the electron microscope.
Light microscopes have a problem. As a rule, you can’t resolve features smaller than the wavelength of the light you’re using. Since this might be in the neighborhood of 600 nanometers for visible light, you have no real hope of seeing smaller things, or even of seeing objects a few times bigger than 600 nm very clearly. Bacteria can easily be this small, and viruses are smaller still. To see them clearly you’d need a smaller wavelength light. Ultraviolet light or x-rays might fit the bill, but they also tend to be very difficult to use in microscopes and their photons are too energetic to see many things without destroying them in the process.
Fortunately the wave nature of matter gives another option: use electrons instead. The de Broglie wavelength of a particle of matter is given by Planck’s constant divided by the momentum of the particle. Doing a little bit of math, we find out that an electron accelerated by just 2 volts has a wavelength equal to about 600 nm. Cranking the voltage up to an easily achievable 15,000 volts means the electron wavelength is less than a tenth of a nanometer. Viruses and bacteria aren’t so difficult to see clearly at this resolution:
While in theory the wavelength can be made as small as you like by cranking up the power, there’s not much point. The most advanced electron microscopes can make out individual atoms as blurry fuzzballs (which they are), and there’s simply no well-defined structure to “see” at lower scales. There’s no shortage of things to learn at smaller scales, which is why we keep building bigger and bigger particle accelerators to probe those scales, but spatial structure isn’t really one of those things.