BTW, as my passed down middle name indicates, I come from a long line of Grants, so perhaps that's why you tolerate me???
Back to John now, below is the verbatim answer I received from Zack on your question regarding gamma ray microscopes - which I enjoyed immensely. I hope it satisfies you as well!
Ooh! What a fun question.
It is such a good idea that Werner Heisenberg himself did a thought experiment using a gamma-ray microscope in order to derive an early version of the Heisenberg uncertainty principle.
So, can we build it? Well the short answer is yes and here it is: http://www.spring8.or.jp/wkg/BL31LEP/in ... mmary_view
And we also have a gamma ray telescope: https://fermi.gsfc.nasa.gov
Just to make sure definitions are clear, when we say gamma rays, we usually mean photons that were emitted by atomic nuclei as a result of nuclear processes. The reason the electromagnetic spectrum has a region called “Gamma Rays” is because most of the natural radiation that occurs in that portion of the spectrum is caused by radioactive decay emission. However, many gamma rays have energies that occur all the way down into the X-ray band. However, the point is clear, why can’t we just use *really* high energy (short wavelength) photons in order to get resolutions small enough to see atoms?
While it is true that as you go to smaller wavelengths the theoretical resolution of the microscope gets better and better, at some point other engineering considerations become dominant. Just from an engineering point of view, gamma rays penetrate matter easily and so designing a mirror system to focus them can be a bit tricky.
Now, if you use an electron instead of a photon, then you can get an electron to have wavelengths much smaller than an atom quite easily. In fact, it only takes a few thousand volts to do that. The electron microscopes I use are using electrons between 80,000 and 300,000 V. At 300,000 V, the wavelength of the electron is about 2 picometers — already much smaller than a hydrogen atom (which is small for atoms). For electron microscopes, the best resolution we’ve seen is about 50 picometers, and the limit is not caused by the wavelength of the electrons but other factors influencing how well you can focus the beam and so on. As it turns out, our very own microscopy facility here in Berkeley is on the cutting edge of high-resolution electron microscopes with a number of record firsts. For example, see this: https://physicstoday.scitation.org/do/1 ... 0691/full/