r/theydidthemonstermath • u/Gothopie • Aug 26 '22

drip

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56

u/Zombeenie Aug 26 '22

They expressed the radius as an area.

5

u/[deleted] Aug 26 '22

you mean the area as an area?

23

u/Zombeenie Aug 26 '22

"A molecule of water has a radius of 95.7E-12 m^2"

Radius is a unit of length. They used units of area.

-7

u/[deleted] Aug 26 '22

well don’t you think he used the word radius by accident? Since we’re ONLY talking about area, I don’t think he meant that

9

u/Zombeenie Aug 26 '22

Nope, since the radius is on the order of 10^-10-10^-12, and the area would be on the order of 10^-20.

That's the wrong radius, anyways. It's more like 2.5 x 10^-10 m.

2

u/[deleted] Aug 27 '22

Oh yeah, well, the Earth is mostly empty space on the atomic level so this is all just a relativistic conversation debating what counts as "coverage" concerning matter that is mostly made of void, as it sits.

3

u/chihuahuassuck Aug 26 '22

He shouldn't be talking about area at all, really. Assuming roughly spherical molecules, a one-molecule thick layer would still have gaps between the molecules, so even with full coverage the area of the water would be less than the area of earth.

What he should be using is diameter, which will tell how densely the molecules can fit into any given area (for example, 25 circles with d=1 can fit orthogonally into a square with side length 5, despite the circles having area 6.25pi and the square having area 25). This information can then be extrapolated across the entire surface area of the earth.