A single electron (and positron) annihilation, is my face melted?

Question

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.

Answer 1

It turns out there is a good way to estimate this.

In PET (positron emission tomography), the patient is injected with a radioactive tracer that emits positrons (hence, the name). These positrons annihilate with electrons, and emit two 511 keV photons. Detecting these photons, one can estimate the location of the radiation. Doing this many times over, you can create an image of the tracer uptake - used in a wide variety of medical diagnostics.

So no, one annihilation won't kill you - even when it happens inside your body. Typical injections are on the order of 10 mCi (370 MBq) - so even 370 million annihilations per second won't kill you.

Long before the "energy" will kill (by cooking you), it is the ionization properties that will get to you. The typical lethal dose is considered to be 20 Gy - J/kg or about 1 kJ spread evenly over your body. Much lower levels would make you quite sick. The amount of damage done by radiation to individual organs changes quite a bit - some organs are much more sensitive than others. In radiation therapy, they try to deliver a local dose of about 70 Gy to tumors, while sparing the surrounding tissue; but they do this in "fractions" - giving just a little bit of dose every day for several weeks in order to give the tissue a chance to recover. And that is usually enough to make people feel pretty sick.

You should expect that you will really notice the effects of 1 J of radiation being delivered "locally" (say, to your hand). That would correspond to 6 x 10¹² electrons. Not a crazy number.