Will we eventually be able to create powerful enough electron microscopes that we could see atoms and subatomic particles?

Answer 1

Not microscopes per se. Microscopes are used to view the fine details of molecular matter, so after going beyond the atomic, it is no longer considered microscopy. Some electron microscopes can resolve single atom detail.

For inspecting subatomic particles, we use particle accelerators, which work similarly to electron microscopes, in that they use a beam of high velocity particles (sometimes electrons) with wavelengths on the order of the size of the details we want to investigate. These high velocity particles interact with the subatomic particles to produce diffraction patterns, which are then used to calculate the original arrangement of the subatomic particles. But unlike a microscope, we cannot see a "snap shot" of the inside of a nucleus. The arrangement of particles in a nucleus is constantly changing, and the electrons only hit it one-at-a-time, so instead we obtain a probability for the locations of subatomic particles relative to other subatomic particles.

It might seem a little complicated, but think of it like throwing stones at a moving marry-go-round. If you plot out where the stones land, you will eventually see that the marry-go-round is a plate with a bunch of point masses arranged at multiple radii. Throw even more stones, and you might be able to determine the speed at which the marry-go-round is turning, and the locations and number of the masses. Throw a whole lot of stones even faster, and you might be able to tell what the individual masses look like. Now think about throwing all of those stones, not at a single marry-go-round, but many marry-go-rounds, all of the same model, and it will be the same as a particle accelerator.