Cecil made another error when he estimated 100 million molecules per snowflake. By my calculations, it’s actually closer to 3.15x10^20 molecules per snowflake.
Will it never end…
Welcome to the Straight Dope Message Board, K2, glad to have you here.
I think you are referring to How can they be sure no two snowflakes are alike? It’s helpful to provide a link to the column being discussed, so that others can have a clue what the heck you’re talking about.
Also, since this is about Cecil’s column, not about a Staff Report, I have moved it to the appropriate forum.
(edited to fix link)
[Edited by Arnold Winkelried on 06-15-2001 at 09:38 AM]
K2Rage101, what assumptions / numbers did you use to come up with your result? Maybe that would help fuel the discussion as to which figure is more accurate.
OK, let’s approximate that a snowflake is a disk, about, oh, let’s say 2 mm in diameter, and about .1 mm in thickness. That gives us a volume of 310[sup]-4[/sup] cubic centimeters, and water has a density of 1 g/cm[sup]3[/sup], so that’s also 310[sup]-4[/sup] grams. Water has a molecular mass of 18, so we’ve got 10[sup]23[/sup] molecules in 3 grams, or 10[sup]19[/sup] molecules in a flake. It’s only one and a half orders of magnitude off from K2Rage101’s calculation, but there’s probably that much size variation between individual flakes.
I suspect that Cecil was just using “a hundred million” as shorthand for “a friggin’ huge number”. Remember, he’s writing for the unwashed masses, here, many of whom can’t count above ten without taking off their shoes. This suspicion is born out by his use of the quantity “gigajillion” later in the sentence, and his followup makes clear that he was fudging.
Thanks Dexter for getting me straightened out =)
Sorry for the ambiguity here - honestly, I didn’t think anyone would take notice of my thread. Here’s the way I figure:
Cecil states that it has been CALCULATED that there are 1,000,000 flakes in a 2’x2’x10" section of snow (24"x24"x10" = 5760in^3) which is easily converted to cm^3 (2.54cm = in) for 94389cm^3.
This volume cannot be converted directly to grams because we get 10" of snow for every 1" of rain (snow is ~10x less dense than liquid water) So… 94389 x 0.1 = 9439cm^3 = 9439g.
Using water molar mass = 18 we get 524 moles of H20, which can be converted to molecules using Avagadro’s number - 3.158x10^26 molecules water. Divide this by 1 million flakes and we get…
3.158x10^20 molecules per flake.Of course, the aggregate density of snow is also hugely variable. It can be as low as .1, if it’s really fluffy, or nearly one, if it’s been packed hard. Snow is a very imprecise thing.
This still doesn’t get us close to Cecil’s number, but I still say that he didn’t intend for precision, there.