Tuesday, January 01, 2013

Don't worry about the Kilogram overmuch

The link on twitter from mentalfloss.com raised my eyebrows: "The Not-So-Perfect Kilogram and Why the Metric System Might Be Screwed"

For a science person like me, my first reaction was bemused curiosity. Then I read the article. The things mentioned have been discussed many, many times by physicists and others interested in pinning down our system of measurement into universal constants. It's kind of like how our great grandparents often wrote their recipes to specify the quantities of things using the tools they had available. A "cup" of sugar might have meant your great grandmother Ingrid's favorite coffee cup (actual volume: 9.5 oz), or great-great-granddad's tin cup that he brought back from Germany (actual volume 6 oz). Making a recipe with the wrong cup might mean very sweet - or very sour - lemon merengue pie if made with a standard measuring cup (8 fluid ounces or about 240 mL).

Now imagine these vagaries applied to the world of the very large, or very small, or very dangerous. Not the kinds of wobbles that lend any sense of certainty to measurements of the natural world.

So back to the article itself. The headline is absolute sensationalism. And I find it utterly annoying. The kilogram is not doomed to oxidize away, or be handled into oblivion. We have a universal constant - Avogadro's Number to represent exactly how many atoms are in a certain amount of something. In this case, that certain amount is called a "Mole." Pronounced like the burrowing mammal (or the benign skin tumor), not the sauce. One Mole of Carbon contains 6.022x1023 atoms of carbon. That's Six Hundred Two Septillion atoms...

And one Mole of pure Carbon-12 (a carbon atom with 6 protons and 6 neutrons) would have a mass of 12 grams. A Mole of carbon you might pull out of a tree or something just lying around would have a mass slightly larger (12.011 grams) because there is a small fraction of Carbon-13 and Carbon-14 knocking about and getting involved with all of the regular Carbon-12. So defining the Kilogram in terms of an absolute number of pure atoms is easy and already done. But establishing this easy-to-reproduce-in-your-lab standard is much trickier, since atoms are so small and there are so many atoms in a mole.

If using Platinum (Pt, atomic number 78) one Mole would have a mass of 195 grams. So if you had 5.128 Moles of Platinum, you'd have your perfect kilogram (within a few hundredths of a percent due to rounding). Incidentally, that works out to about 40 milligrams - a bit more than the difference of 0.05 milligrams mentioned in the above article. But not bad for zero dollars and about 5 minutes of scratching around with a calculator...

Platinum, however, is a rather expensive material - most of us don't have that much platinum around. And on today's market, 1 Kg of Platinum would get you almost \$50,000. But what about Silicon? There's lots of Silicon - it's the second most common element on (and in) the earth. 1 Mole of Si would have a mass of 28.09 grams, therefore you'd need about 35.6 Moles to get your Kg standard. So how could we count all those atoms? By using x-ray crystallography, we can get a pretty good estimate on how many atoms there are in one cubic centimeter (the meter, by the way, is defined in terms of the speed of light and the distance travelled in one second - the second being defined as 9.2 billion oscillations of a Cesium-133 atom, but I digress). Once we know how many atoms in a given volume we have, all that remains is to manufacture that perfect object with that precise volume. We're talking "perfect" here - beyond even "repaired hubble telescope mirror perfect." But that's more of a limit of technology than theory - I've read about some of these attempts at a perfect silicon sphere in a science magazine a few years ago.

And so, in the end, I was largely unimpressed by the suggested immediacy of the little bit of trivia, but I'm glad things like this do get attention. Because efforts to establish more reliable measures and better define these "constants" affect our everyday lives. But don't throw out your Ikea custom-molded measuring cups in hopes of a more accurate polished Silicon version. For most of the time, what we've got in our cupboards is more than enough to make a good pie.