# More atoms in a grain of sand than stars in the observable universe?

in this video https://www.youtube.com/watch?v=AbgcITHmXBI the guys in the end says that there are more atoms in a grain of sand than stars in the (observable) universe. My estimation with this: 100 bilions of galaxies 100 bilions of stars per galaxy

So, 10000 bilion of bilions of stars in the observable universe=$10^{22}$

For a typical grain of sand (size 1mm) made of Si02 , the estimate is $10^{19}$ atoms... If a grain is a fraction of mg, 1 g of grain has truly more atoms than stars in the universe.

Do you have some good estimate?

• I think you've discovered that this seeming aphorism and ones like it need to be taken with a grain of salt. How big a grain of salt? Perhaps one that contains at least as many stars as the observable Universe. – WetSavannaAnimal Mar 21 '17 at 12:10
• Whether this just a bit too neat a comparision, and so it's easy to remember, I don't know: If an apple were magnified to the size of the Earth, then the atoms in the apple would be approximately the size of the original apple. from en.wikipedia.org/wiki/Atom – user146020 Mar 21 '17 at 13:04

The number of stars in the observable universe has been discussed in the question How do we estimate $10^{23}$ stars in the observable universe? My answer to this does little more than repeat the conventional wisdom, but Pulsar's answer presents a very interesting alternative approach that ends up at about the same number. The number of stars in the observable universe turns out to be around $10^{23}$, but this is a pretty loose approximation and it could easily be an order of magnitude higher or lower.

The number of atoms in silicon dioxide can be rather more precisely determined since the molecular weight of silicon dioxide is $60$, so $60$ grammes contains $3 \times 6.023 \times 10^{23}$ atoms, which is about $1.8 \times 10^{24}$ atoms.

So $10^{23}$ atoms is about 3.3 grammes of sand. But bear in mind that order of magnitude uncertainty in the number of stars.

• So the guy in the video is wrong – Saladino Mar 21 '17 at 12:15
• @Saladino: it would have to be a very big grain :-) – John Rennie Mar 21 '17 at 12:16
• Ok, thank you :) (but for definition a grain is less than 2mm) – Saladino Mar 21 '17 at 12:34

What the guy in the video was saying was most likely just an estimate, not an exact figure. No one knows how many starts there are exactly in the universe, but your guess of 10^22 seems fair.

To find how much grain of sand you would need to have 10^22 atoms, simply using molar mass conversions. Use Avogadro's Number to go from 10^22 atoms to # of moles. Then use the molar mass of SiO2 to go from # moles to grams. My calculations (with the units in bold canceling each other out):

10^22 atoms * (mol / 6.02 x 10^23 atoms) = 0.0166112957 mol

0.0166112957 mol * (60.1 g / mol) = 0.9983388704 g

So going by your estimate of 10^22 stars in the universe, you would need about 1 gram of sand to have an equal number of atoms (assuming the sand is completely made up of SiO2).