Unexpectedly Intriguing!
August 28, 2020

There's a fun project going on among math bloggers and vloggers, who are presenting their favorite big numbers that are larger than one million, tagging their contributions with the #megafavnumbers hashtag.

Since we periodically cover math stories, our contribution is 602,214,076,000,000,000,000,000, which if you've had chemistry, you'll probably recognize more quickly in its scientific notation format: 6.02214076 x 10²³. It's Avogadro's constant, which tells us approximately how many atoms or molecules there are in a mole of a substance. A mole is the number of grams of a substance that is equal to its molecular weight, or rather, the number of protons and neutrons in its component atoms or molecules.

It was originally indexed to the mass of Carbon-12, which has 6 protons and 6 neutrons. One mole of carbon-12 therefore weighs 12 grams.

It used to be that the number of atoms in a mole wasn't exactly known, because counting the number of atoms in 12 grams of carbon-12 isn't as easy as it sounds. Scientists had narrowed the range of potential values down to fall within 100 quadrillion atoms of 602,214,150,000,000,000,000,000 (602.21415 sextillion), but on 20 May 2019, the International System of Units (SI) body arbitrarily fixed the value of Avogadro's number to exactly 6.02214076 x 10²³. We still don't know exactly how many atoms there are in an actual mole of a substance, but we now have a close approximation that the world's measurement experts have officially endorsed.

Avogadro's constant can be found in more places than just chemistry. Astrophysicst Alex Howe's #megafavnumbers contribution points to where it is used in statistical mechanics.

At this writing, there are over 153 entries in the #megafavnumbers video list, which take on illegal primes, the monster, and the case of too many lottery winners, among others! If you've run out of binge-able videos to watch during the pandemic, why not add a bunch of videos about really big numbers to your playlist? We'll award extra points if you watch them in order from lowest to largest....

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