Gammons, salt and bond's length

Today (on 2007-09-29) I was having supper here in my little room and was currently eating a slice of bread with gammons, seasoned with some salt. When it came on me that I wanted to know how many ions, placed next to each other, make up one edge of one of these little salt grains I was seeing. This question had bothered resp. interested me at some times before: how small are atoms, measured by everyday objects, so as to get a “feeling” for the size of atoms. This time I decided that I wanted to know … .

Some quick research in the Internet gave the first results: in the ion grid of a crystal, the grid distance is the result of summing up the ion radii of both ions … an ion radii are measured thus that the attractve and repulsive forces of two ions are in equilibrium when placed in the distance next to each other that is given by the sum of both ion radii. For Natrium Chloride (Na+Cl, i.e. salt), the sum of the ion radii is 0.276 nm [Ernst-Georg Beck: Chemiekurs 2002, Kap. 2.1 Ionenbindung]. So this is the distance from the center of one Na+ ion to the center of its neighbour Cl- ion, i.e. the grid distance.

So now let’s calculate how many ions make up the edge of a 0,5mm salt crystal cube:

0.5 mm / 0.276 nm = 0.0005 m /
0.000000000276 m = 1 811 594 ions

How to imagine that numer? Imagine a square with 1.8 kilometers edge length, partitioned into 1mm² small squares. Then each square resembles one ion, and the big square the face of the salt crytal with 0.5 mm edge length. In my imagination up to this calculation, I would have rather thought of a square with 100 m edge length as an analogy, i.e. I thought that atomic structured were about 10 times larger.

Now, thinking of the way our body is made up of structured where single molecules matter (e.g. DNA), I marvel at God’s awful excellence in fine mechanics. He really an deal with structures of that size, while we have a hard time to even find an analogy for them!

BTW, this is the authentic picture from the rest of the slice of bread I ate when thinking about this salt crystal thing 😉

Start date: 2007-09-29
Post date: 2007-10-01
Version date: 2007-10-01 (for last meaningful change)







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