More atoms in a grain of sand than stars in the universe.

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Minerva
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More atoms in a grain of sand than stars in the universe.

Postby Minerva » Thu Mar 20, 2014 6:41 am UTC

This is a bit of a quick SWOTI question. I'm fairly confident of the answer, but I just thought I'd throw it open here for peer review, feedback or discussion.

Claim: There are more atoms in a single grain of sand than all the stars in the universe.

Discussion: The number of galaxies in the observable universe is not exactly known, but it's about 100 billion, maybe closer to 200 billion. Anyway, in terms of order of magnitude, we'll take it to be 1011. Some galaxies are bigger and some galaxies are smaller, but the average number of stars in a galaxy is also on the order of 1011. Therefore, the number of stars in the universe is on the order of 1022.

How big is a grain of sand? Let's guess, say, 1 mg, although a grain of sand is hardly a well defined unit of measurement. Let's suppose that the sand is chemically pure SiO2 for the sake of argument. At a molecular weight of about 60 g/mol for SiO2, 1 grain of sand is of the order of 10-4 mol, and therefore the number of atoms in a grain of sand is on the order of 10-19. (There are 3 atoms per SiO2 unit, which we ignore.) Hence there are not more atoms in a grain of sand than there are stars in the universe, in fact there are a few orders of magnitude less.

What do you think?
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Re: More atoms in a grain of sand than stars in the universe

Postby lorb » Thu Mar 20, 2014 9:18 am UTC

There was a relevant what-if. This chart that was mentioned tells us that we need to be clear about what we mean when we talk about a "grain of sand". It has a "number of grains per mg" column which runs from below 1 to above 1000 for sand, so there is 3 to 4 orders of magnitude in mass-difference just between a grain of "very fine" and a grain of "very coarse" sand. The number of stars in the universe is also just an estimation. So if you pick a very big grain of sand and a very conservative estimate for the number of stars, you can get a bigger number of atoms.
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thoughtfully
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Re: More atoms in a grain of sand than stars in the universe

Postby thoughtfully » Thu Mar 20, 2014 1:19 pm UTC

If one defines Universe to include contiguous bits of spacetime that aren't observable, the stars win by many orders of magnitude, assuming the physics is similar throughout our bubble. I suppose that's an unfair definition, if we want to give the sand a sporting chance!
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Re: More atoms in a grain of sand than stars in the universe

Postby Gammashield » Fri Mar 21, 2014 8:57 pm UTC

I admit I've always found it a bit of cute serendipity, that there are "about a mole" of stars in the observable universe (where 'about' is defined as 'within two orders of magnitude or so', which is a *very* generous 'about'... but these are some stupidly big numbers, so the fact that it's even *that* close is funny). It casts a different light on the old 'the universe is huge' trope. It's not just huge. It's *Avogadro* huge.

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Re: More atoms in a grain of sand than stars in the universe

Postby tomandlu » Sat Mar 22, 2014 2:10 pm UTC

If one stuck to stars observable from our solar system, does the sand win?
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Re: More atoms in a grain of sand than stars in the universe

Postby thoughtfully » Sat Mar 22, 2014 3:44 pm UTC

If you mean resolvable as individual stars, probably. But the observable Universe is more or less observed (with the usual caveats about looking into the past), although it's mostly resolvable down to individual galaxies. I don't think an appreciable portion is blocked by dust clouds and the like. But IANAA.
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