The neutrinos that are generated from the supernova are in the order of Peta eV, which is very large; when they reach the earth surface and get contact with earthly bodies, do they make any harm, if not why ?
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A neutrino could cause a beta decay in a nucleus moving an element one step further in the periodic table and typically make it unstable and radioactive. I hope experts will answer how this probability depends on the neutrino energy. – safesphere Oct 27 '17 at 19:58
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Here's a relevant "what-if?" article. It cites a paper by Andrew Karam : "Gamma and neutrino radiation dose from gamma ray bursts and nearby supernovae" .
According to this paper, the neutrino radiation dose at a distance of one parsec from a supernova would be around half a nanosievert. At $2.4 \mathrm{AU}$, the radiation dose from neutrinos alone would be lethal ($\mathrm{4 sieverts}$).
If Spica (one of the nearest stars to the Sun that has enough mass to end its life in a Type II supernova) went supernova, we would get about $ 4 Sv ⋅ (2.4\mathrm{AU}/250\mathrm{ly})^2 ≈ 100 \mathrm{fSv}$ of neutrino radiation. This represents less than 4 milliseconds of the average background radiation.
From the paper :
The average energy of neutrinos released in supernovae explosions is between 5 MeV (Schramm and Brown 1990) and 15 MeV (Sutaria and Ray 1997).
It's not clear where your $\mathrm{Pev}$ order of magnitude comes from. Scaling the previous quantity by $\mathrm{1PeV/(15MeV)}$, the neutrino radiation dose would be around $6 \mathrm{µSv}$. This quantity would be perfectly measurable but not harmful.
Neutrinos are extremely hard to detect, it makes sense that even highly energetic neutrinos from a few parsecs away would not interact with our body in any way.
The effect of other particles from a near-Earth supernova would be much stronger and potentially dangerous.
Eric Duminil
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2Might be useful to compare this with the effect of other near Earth supernova effects. – StephenG - Help Ukraine Oct 27 '17 at 20:40
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This is a "knock me over with a feather" scenario. Even moles and scientific notation would have a lot of trouble calculating the amount of neutrinos required to even interact with one of our atoms. (We're assuming all of them hit space somewhere in your general volume.)
Camo_man
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$\rm PeV$ neutrinos actually have a much larger interaction cross section than solar neutrinos. It doesn't take many neutrinos at that level to get some interaction with your atoms. – Chris Nov 05 '17 at 09:17