Alright, right here it is, the an initial instalment the – the very anticipated – Craig’s Questions. The an initial question came around following a conversation with someone that is researching maths. That (Andy) casually reduce the adhering to phrase right into the conversation around numbers, as a statement expected to inspire wonder. The explain did more than simply that because that me though, it increased my curiosity and I feel compelled to sit down and work it out for myself. But here’s the point to consider prior to we go any kind of further, numbers, past a details point, shed their meaning to us. Ns don’t yes, really think our brain works well with visualising numbers past the thousands and it most likely struggles also with that. Because that example, I understand that ns can’t visualise 10,000 apples. I know the ide of the number yet I couldn’t kind an accurate photo of the in my head. Would certainly it be as tall as me if they to be still in their cases? (Probably.) How large would it be if we staked lock to just my height (6 ft)? this answers simply elude my intuition and, i suspect, you’re no different. The adhering to question takes benefit of that and also forces us into the worlds of Avogadro’s number, maths and also straight up comparisons. At an initial these types of explanation or questions seem impossible to answer and if anyone delivered an answer confidently enough one method or another, you might just it is in inclined to think them and also move on v your day. Hopefully you will do it realise that working it out is much more fun.

You are watching: How many atoms in a grain of sand

Read this question, think about it and have a guess (no cheating or functioning it the end for yourself, we’ll run v the maths together later on). I’d love to recognize what you thought. To do this even an ext fun, comment (below) or tweet me (
Sci_McInnes) your intuitive guess now prior to we relocate on. I’d genuinely love to recognize what girlfriend think!

So below we go, the very first question:

“Is that true the there are an ext atoms in a serial of sand 보다 there space grains of sand ~ above the Earth?”

Damn, that sand look at nice. Picture credit: Craig McCubbin

### So, very first off, to the (chemist’s) simple part: how numerous atoms space there in a serial of sand?

To do this, we have to know around Avogadro’s number (nice video). This number tells united state how countless atoms there room in one mole of a problem (i.e. How plenty of atoms there are in 12 grams the carbon-12, because that example); the prize is 6.022×1023. That’s a huge number. We use Avogadro’s number to provide us the number of atoms in a grain of sand in the following method (pssst, skip this if you don’t prefer maths, just look because that the various other blue “pssst”.):

Avogadro’s number  =number of molecule in gram that sand (1.004×1022)

Weight that one molecule the sand

We then multiply this by three as there are three atoms in every molecule. The price is 3.012×1022.

So now we know the variety of atoms in a gram of sand, we’ve got to figure out how many grains that sand there space in a gram and also multiply that by the number of atoms in that same weight.

If a medium grain that sand takes increase 0.5 mm of an are (0.0005 cm3) and 1 cm3 of sand weighs ~2.8 g climate one tool grain that sand weighs around 0.0014 g (1.4 mg)

Now: number of atoms every gram x variety of grains per gram = variety of atoms in one grain

0.0014 x 3.012×1022 = 4.33×1019

(Pssst, pay fist here) That method that there room 43 quintillion atoms in one serial of sand. Damn, it is a big number.

Now, how many grains that sand are there on the Earth?

Image credits: Craig McCubbin (wikimedia)

This bit was a tiny trickier. I couldn’t just straight out guess it since I don’t have a map or any kind of concept of how deep the grains of sand go in a desert, or a beach, or even a sandpit because that an Olympic game of beach volleyball. Therefore I had actually to look it up and also the estimates vary from in between 7.5×1018 throughto 7×1021. It appears that every one of these estimates are skipping the deserts and the ocean, so i think that we can say that even the top estimate here is fairly conservative. So let’s compare the 2 numbers and see i m sorry is bigger; 7 sextillion or 43 quintillion? that’s right, you guessed it, that 7 sextillion (7×1021).

So that means that, also being fairly conservative with our estimates, and to price our original question, there are more grains that sand top top the planet than there are atoms in one grain of sand, through at the very least three assignment of magnitude. Mind blowing! I have to say, regardless of the outcome, the mere reality that we can contemplate these inquiries with some level of precision is, really, the truly mind-blowing thing and also that’s why I chose to write around it today; science is awesome.

See more: How Much Weight Can A Pallet Hold, How Much Load Can My Pallet Carry

Thanks because that the constant slew the “Craig’s Questions” go to Sam (
_whitewashed) and also the countless interesting conversations v Kieran and also Andy. If you have a question that you’d choose me come answer, tweet me (
Sci_McInnes) or email me c (dot) mcinnes (dot) chem (at) gmail (dot) com and I’ll do my finest to price them.