Batman's Last Fermi Problem

Mr. Freze BatmanDiamonds are just carbon all bound together. Each carbon is bonded to 4 other carbons. If you think about that a bit you will see that means there are TWO bonds for every atom (imagine/draw a fairly large grid - count the number of nodes/intersections and count the number of connecting lines. If this ratio isn't exactly half it's because the edges of the grid might cause trouble [if you draw it smarter or bigger it will get closer to 2]). That means that there is 3eV of energy available for every atom. Let's assume Mr. Freeze's gun can access all that energy.

Now that we know how much energy we can get from each atom we need to guess how many atoms are in a diamond. To do that we need the mass of the diamonds. When jewelers talk about carats their really just talking about mass --- 1carat = 0.2g. Maybe you know what the carats of some famous diamonds are? 100 carats is a BIG diamond so let's say 30 carats or in grams: 30 carats * (0.2g / 1carat)= 6g.

Mr. FreezeHow many atoms are in 6g's of diamond? Well what's the atomic weight of carbon? If you don't know, can you imagine where carbon is on the periodic scale? It's near the beginning but not first and it's nowhere near the end. So say between 1 and 100. You could then say 10g / mol. OR you could have memorized your periodic table and remembered the value is actually 12 g/mol but really what's the difference?

So now we know the number of atoms in the diamond is about 6g * (mol/12g) * (6*10^{23}atoms/mol) = (36/12)*10^{23}atoms = 3*10^{23}atoms. And since we guessed about 3eV is released from each of those which means the energy is (3eV/atom) * 3*10^{23}atoms * 1.6\times10^{-19}J/eV = 9* 1.5 *10^4J = 13.5 * 10^4J = 10^5J.

Is that alot? We said in previous questions that a person uses 3.5*10^3J every day and the energy of a subway train is 10^7J. The energy Mr. Freeze can get from a diamond is somewhere in between.

And here ends the Fermi Problems part of my Batman training - at least on the blog. But if you have any superhero Fermi problems that you think I should do on Building Batman just leave a comment and I'll give them a whirl.

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