# Neutrino Query

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I understand that around 65 billion neutrinos pass through every square centimetre of human skin (or any other skin for that matter) per second. I also gather that a human being can expect to be struck by an individual neutrino perhaps once or twice in a lifetime. These statistics, if true, are remarkable on several counts. Nevertheless, in order to get an handle on what this continual neutrino blitztkrieg really means at an atomic level, I've been trying to find out what the average density of atoms there are in a given square (not cubic) centimetre of human skin - but no luck so far. Does anyone have even an approximate answer to this admittedly obscure question? Many thanks.

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Water has density 1 g/cm^3

Water has 18.016 g/mol

Divide them

1 g/cm^3 / 18.016 g/mol = 0.0555 mol/cm^3

1 mol = 6.022141*10^23 molecules or particles

0.0555 * 6.022141*10^23 = 3.343*10^22 molecules.

Density of fat man is slightly less or equal to 1 g/cm^3 (therefor floats on water, especially sea water).

If you divide 1 cm^3 by number of molecules in that volume, you will have approximate average volume of single molecule.

From this you can get average radius,

and make calculation of single slice of such molecules with 1 cm^2 area (and thickness of single diameter of average volume).

Or you can calculate cubic root of 3.343*10^22 = 3.22*10^7 average molecules in 1 cm straight line.

3.22*10^7 ^2 = 1.0377*10^15 in 1 cm^2, average.

Edited by Sensei
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Just as a wild approximation (with no checking facts or calculators so lotsa guessworking)

1. most of body is water

2. molecular mass of water is 18 g/mole

3. mass of cubic centimetre of water is 1 gram

4. no of water molecules per cubic centimetre is avogadro divided by molarmass - ie 6e23/18 = 3e22

5. assuming rough three dimensional lay out that is cube root of 3e22 each direction

6. cube root 3e22 is cube root 30 time cube root 10e22 = 3e7

7. number of molecules in top square of cube is 3e7 times 3e7 ie 9e14

8. three atoms per molecule so roughly 3e15 atoms per square centimetre

Edited by imatfaal
cross posted with Sensei - hopefully result is in same ball park
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I understand that around 65 billion neutrinos pass through every square centimetre of human skin (or any other skin for that matter) per second. I also gather that a human being can expect to be struck by an individual neutrino perhaps once or twice in a lifetime. These statistics, if true, are remarkable on several counts. Nevertheless, in order to get an handle on what this continual neutrino blitztkrieg really means at an atomic level, I've been trying to find out what the average density of atoms there are in a given square (not cubic) centimetre of human skin - but no luck so far. Does anyone have even an approximate answer to this admittedly obscure question? Many thanks.

You can't strictly speak of a "density" without using volume, But I'll interpret your question as being how many atoms would there be in a one atom thick area of 1 cm^2. An admittingly rough estimate would be ~3e10 atoms.

And while this my seem to be a lot, you need to consider that neutrinos only interact with the nuclei of atoms, and the nucleus of a atom is much, much smaller than the atom itself. The total combined cross sectional area for the nuclei of those 3e10 atoms works out to be only 6e-19 cm^2. To give you an idea of what this means, imagine a target with a 1 cm diameter. Around it draw a circle with a radius of 64.5 kilometers. The target represents the total cross section area of the nuclei and the outer circle the 1 cm^2 surface area of the skin.

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And while this my seem to be a lot, you need to consider that neutrinos only interact with the nuclei of atoms,

Search for neutrino-electron scattering on Google

Neutrino-nuclei interaction result in turning nuclei to other isotope.

With the most well known Cl-37 transforming to Ar-37 (and then back to Cl-37, after electron capture, Argon-37 + e- -> Chlorine-37 + Ve + 0.813874 MeV).

(it needs neutrino with energy equal to or higher than 814 keV, so proton-proton fusion neutrinos with up to 420 keV are not triggering it)

Edited by Sensei
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Yes, I should have used 'concentration' rather than 'density'. I stand corrected. So I guess then that if 1 cm2 of skin contains (in round figures) a quadrillion atoms, this means that there's an excess of around 15,000 more atoms than those neutrinos passing through this same area per second. But as Janus points out, a given 'atom' consists mostly of space, which explains why the strike rate is so low. (At some point I'm going to sit down and calculate exactly what this means at a sub-atomic level). Still, I'm intrigued as to why there appears to be such a glaring contrast between the strike rates of neutrinos and (say) cosmic rays. Yes, I surmise that neutrinos are chargeless and nearly massless particles, while cosmic rays, which being composed mostly of high-energy protons, are both enormously more more massive and carry a charge. Yet if atoms are comprised largely of emptiness, I'm left wondering why cosmic ray nuclei are many times more damaging in a biological context. Or am I missing out on something here?

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The other important factor is that neutrinos only interact via the weak force, while others interact via electromagnetic force, as well.

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Yes, I should have used 'concentration' rather than 'density'. I stand corrected. So I guess then that if 1 cm2 of skin contains (in round figures) a quadrillion atoms, this means that there's an excess of around 15,000 more atoms than those neutrinos passing through this same area per second. But as Janus points out, a given 'atom' consists mostly of space, which explains why the strike rate is so low. (At some point I'm going to sit down and calculate exactly what this means at a sub-atomic level). Still, I'm intrigued as to why there appears to be such a glaring contrast between the strike rates of neutrinos and (say) cosmic rays. Yes, I surmise that neutrinos are chargeless and nearly massless particles, while cosmic rays, which being composed mostly of high-energy protons, are both enormously more more massive and carry a charge. Yet if atoms are comprised largely of emptiness, I'm left wondering why cosmic ray nuclei are many times more damaging in a biological context. Or am I missing out on something here?

Charged particle, accelerated to relativistic velocity, has enough energy to ionize matter it is passing through.

And it's used all they time to show their traces like in Cloud Chamber particle detector.

Here you can see what happens if you put Gold foil: majority of alpha particles (+2 charge) are repelled, minority pass through foil to the other side:

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Still, I'm intrigued as to why there appears to be such a glaring contrast between the strike rates of neutrinos and (say) cosmic rays. Yes, I surmise that neutrinos are chargeless and nearly massless particles, while cosmic rays, which being composed mostly of high-energy protons, are both enormously more more massive and carry a charge. Yet if atoms are comprised largely of emptiness, I'm left wondering why cosmic ray nuclei are many times more damaging in a biological context. Or am I missing out on something here?

The simple fact that cosmic rays consist of charged particles is the answer in itself. Neutrinos, as already pointed out, interact through the weak force, which is very short range, thus a neutrino needs to get very close to a nucleus for their to be any chance for an interaction. Cosmic rays, are in fact atomic nuclei themselves, with an electrostatic field that extends well beyond themselves. It doesn't have to score a near direct hit on the nucleus, it just needs to pass close enough to pull an electron free from the atom. And since, as I point out earlier, the atomic radius is much greater than the nuclear radius, this is a much, much more likely event.

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The simple fact that cosmic rays consist of charged particles is the answer in itself. Neutrinos, as already pointed out, interact through the weak force, which is very short range, thus a neutrino needs to get very close to a nucleus for their to be any chance for an interaction. Cosmic rays, are in fact atomic nuclei themselves, with an electrostatic field that extends well beyond themselves. It doesn't have to score a near direct hit on the nucleus, it just needs to pass close enough to pull an electron free from the atom. And since, as I point out earlier, the atomic radius is much greater than the nuclear radius, this is a much, much more likely event.

Ah, yes, I understand now. Thanks for pointing this out to me. I had intended to use the image of an incoming comet and a rogue minor planet (of Ceres mass) passing through the solar system as an analogy for the expansiveness of sub-atomic space. But I can see now that this is no analogy at all.

PS. Those cloud chamber shots are astonishing!

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