A gram-molecular weight of carbon is 12 grams. A mole of a substance is the amount in grams equal to the molecular weight of the species. Carbon contains 6 protons and 6 neutrons in its nucleus, a total of 12 atomic mass units, (the electrons are so light their weight can be ignored). If you look up carbon in the periodic table its atomic weight is 12.011 (instead of an even 12) because there are always a few atoms of isotopes other than C12 scattered in it. An isotope is of a slightly different weight because it has 6 protons but more or less neutrons in its nucleus, this throws off the average. Carbon 14 is a radioactive isotope of carbon with 6 protons but 8 neutrons. The number of of protons equals the number of electrons and electrons determine the atom’s chemical behavior. Since all isotopes of a given element are chemically equivalent, it is extremely difficult to separate different isotopes from a sample of an element. That is why the fissionable isotope U235 has to be concentrated in “enriched” fuel or weapons grade Uranium because the more common isotope (U238) is not fissionable.

The system of gram-molecular weights was devised so it would be possible to estimate weights of atoms or molecules. For example, a mole of hydrogen gas (H2, because there are two hydrogen atoms in each molecule) weighs 2 grams. A mole of oxygen gas weighs 16 grams because there are two atoms of oxygen in each molecule. A mole of H2O weighs 10 grams (1×2 + 8).

Ordinary anthracite coal is almost pure carbon C12), so one ounce of coal weighs about 23.5 grams. Of course, you have to process a great deal of carbon to extract just 5g of the C14 isotope.

This is a good time to review how C14 dating works. C14 is radioactive, its nucleus is unstable, so the amount of C14 in a sample of C is constantly decreasing at a constant rate. C14 has a half-life of 5730 years. C14 is created constantly by cosmic rays colliding with CO2 molecules in the atmosphere. The concentration of atmospheric C14 is in equilibrium, that is, the amount being replaced exactly equals the amount that decays, so the concentration of C14 in the atmosphere is always constant.

When atmospheric carbon is absorbed in organic material (like wood), the C14 continues to decay, but it is NOT replenished by fresh C14 from the atmosphere. So it is possible to determine the age of the wood by determining how much C14 is left in it.

Some other fun facts, a mole of any substance will contain Avogadro’s Number (6.02 x 10^23) atoms or molecules of that substance. If the substance is a gas, at 0 degrees Celsius
and standard atmospheric pressure (STP), it will occupy 22.4 liters of volume.

I would think a 1 gram (5 carat) diamond could contain a very large amount of carbon-14

The density of diamond is 3.50 – 3.53 g/cm3, but most diamond was formed deep in the earth a long, long time ago, so I doubt it has much C14 left in it. I suppose you could make a 5-gram diamond of C14, but you’re not likely to find one in nature.

Extra Credit Homework Assignment:

What is the difference between and isotope and an allotrope? Some allotropes of carbon are diamond, graphite, coal, and BuckyBalls!