To help clarify my understanding of scale in regard to microscopic particle energy levels (specifically, an electron), I came up with this thought exercise:
What would happen if an electron and a positron annihilated one meter in front of my face? Would my face melt? Would I even notice?
I am ignoring the details/difficulties in creating the annihilation scenario. Assume it it possible.
I usually learn the most by making an attempt myself, so here is my crack at an answer:
From Wikipedia, an electron (and a positron) is 0.510998928 MeV/c^2. So their annihilation would yield their sum, conveniently also directly noted in Wikipedia along with a bit of rounding and setting c=1: 1.022 MeV.
Now we need something to compare against. Once again, Wikipedia provides... A flying mosquito is about 1 TeV of kinetic energy. It's definitely looking like I'm not noticing anything. The annihilation expressed in TeV is: 0.000001022 TeV, therefore it would take 978,474 total particles (489,237 electrons, 489,237 positrons) to reach that level of the mosquito. We are at an energy level that under the right conditions could be 'felt'. However, at a meter from my face and the energy being dissipated in an omnidirectional manner, I'm not noticing anything.
Now let's go a little further and (very) roughly estimate how many would be needed to notice. Taking another comparison from this Boom Table, a firecracker is about 100 J, equivalent to about 624,150,965 TeV. We are probably roughly in the realm of something I would feel, but wouldn't hurt me (a true firecracker may due to shrapnel, but no shrapnel with particle annihilation). To reach that level, we need about 3.053577457x10^14 electrons and the same number of positrons.
Are my assumptions and ballpark numbers reasonable? Did I leave out anything significant in my logic?
The number of particles to reach the firecracker energy level is larger than I would have expected. Then again, it's difficult to fathom just how small electrons really are.