Could A Stray Radioactive Particle Collide With an Atom in a Human, Causing a Cascade? I'm not thinking of even particles from a nuclear power-plant or man-made event. If a high-velocity highly-interacting particle made it through all the natural protections that keep life in a non-crispy state and by some highly improbable chance collided with one of the atoms that help to make up a (potentially unfortunate) person.
Would there be any possible deleterious effects? Is that even possible at all (like, do I have a fundamental misunderstanding of this)?
Examples of consequences I hypothesize may be possible (with my limited, and probably flawed knowledge):


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*The momentum being carried by this cosmic particle could (I don't imagine a WIMP could do it) probably destroy at least part of a DNA strand or two, I would imagine that even the sunrays are capable of doing that given the existence of melanoma, etc. So, I'd assume this one's a given but cancer's probably not 99% unlikely, right?

*Could any particle penetrate the skin, and then collide in a highly improbable set of events with some unstable atom in our makeup that could cause a (albeit highly inefficient, and not nearly as spectactular as Oppenheimer's toys) collision cascade of any size? If it could generate any collision cascade event, would it be enough of an event that the subject would even notice it? Or could it be significant enough to explain (if any of the documented cases are even real) the phenomenon of spontaneous human combustion?


I know this seems pretty out there....I just don't understand theses interactions enough, but I do understand them enough to know that I should understand more! :P
 A: Being hit by high energy particles is not far fetched at all. It happens all the time. This is called background radiation.  
Cosmic rays hit atoms in the upper atmosphere and cause cascades there. Most of the action is in the upper atmosphere, but some products do make it down here. Primarily this is a health concern for astronauts.  
Gamma rays and x-rays are also a form of ionizing radiation. These are a health threat. This is why nuclear reactors are shielded, and why doctors minimize the dose of x-rays. (Not getting an x-ray or CAT scan when you need one can be a bigger health threat.) 
A: We are constantly bombarded by muons. Muons form in the athmosphere from primary cosmic rays. About 10000 reach the ground per m$^2$ per minute. 
https://en.m.wikipedia.org/wiki/Muon
A: This is a question about radiation protection. 
High-energy particles from space rarely reach the surface of the earth as they already create a cascade in the atmosphere and little parts of the particle shower can reach the surface of the earth and hit the human's body. 
One could, however, think of a radiation accident in a nuclear power plant or a particle accelerator. In case of very fatal accident somebody could be exposed to high radiation dose respectively to high-energy particles. 
What actually counts for the effect on the human's body is the energy dosis, or even better the equivalent dosis (which also considers the physiological effect of the radiation as a function of the particle type). The energy dosis $D$ is measured in $\frac{J}{kg}$ (ratio of "radiation energy exposed to" to body mass) whereas the equivalent dosis $H$ is 
$$ H = R\cdot D \quad\quad\text{measured in Sievert, shortly}\quad S  $$
where the symbol $R$ reflects the weighting factor corresponding to the type of radiation. For most of the particles the weighting factor $R=1$. It is higher than 1 for neutrons depending of their velocity $R$ can even reach a factor of 20. Nuclei or fragments of nuclei also have a high weighting factor   of 20.
If one is hit by a muon (a result of a cascading high-energetic particle entering the atmosphere), which happens all the time, the effect is very weak with $R=1$, the damage in the human body is small. Most muons which reach the ground are already of low energy, as the energy of the cascading high-energy particle is already distributed over all particles participating in the shower.
In particular the human body is adapted to this type of radiation, so the self-repairing mechanisms on molecular basis will mostly avoid any damage.
Of course one can figure out a very fatal accident at an accelerator or an astronaut hit in outer space by a high-energy particle. 
It depends on the energy dosis or better equivalent dosis the body captures due to the exposition. So it could only be an UV-photon whose total energy (or equivalent) dosis deposited in the body is very small or a very high-energetic particle that starts showering (in this case one has to consider the mean free path of one cascade, (i.e. the distance from the origin of the first shower until a particle of the shower generates a second shower and so on) which is probably larger than the size of the human body, since it depends on Z, the atomic number being usually small in a human body). In particular one has to keep in mind that even high-energetic particles will in most cases only leave energy in the human body by ionisation along their path through the body, i.e. a shower is not triggered at all. In that case the total energy (or equivalent) dosis remains quite small, therefore the bad effect on the body is also small if not negligible. 
So in order to answer your question, if the human body is hit by a high-energetic particle, in most cases almost nothing will happen (trigger of a shower quite improbable, the only energy deposit is through ionisation generated by the particle traversing the human body whose energy deposit is small and its effect can mostly repaired by molecular repair mechanisms).
An exposition of 200-300mS (milliSievert) leads to the acute radiation syndrome (up to now only achieved in nuclear accidents or bombs), more lead to death. Depending on the dosis the effects are sooner or later visible. Low exposition do not show any apparent effect, but can lead later to cancer. In the field of radiation protection a myriad of studies exist on the effect of radioactive radiation on the human body depending on numerous factors, in particular also the energy, the type of radiation and the type of organ exposed. Also the question of lowest threshold of the effect of a radiative exposition is thoroughly studied. You can consult the literature in the field to know more.
A: This is all about levels and risk, not all-or-nothing events. We are all continuously bombarded by background radiation all the time, and this is just one of the sources of potential damage which the cells of our bodies have to cope with. The other sources are chiefly chemical and biological. Background radiation does damage DNA, but in any case most cells will be replaced after some days or weeks and some DNA errors can be corrected owing to the way the genetic code works. The main thing to say is that for most people the background radiation is not the most severe of the stresses their bodies face. The exception would be for those living in high-radiation areas, either from natural sources or from the results of human activity. It is here that in most countries there are public health experts who advise people on the risks.
