There are only a handful of elements that are absolutely essential to all known lifeforms, and carbon is easily the most important. Certainly hydrogen and oxygen in the form of water and other compounds are also essential, but without carbon there simply would not be life as we know it. There are many reasons for that, but that discussion is not for tonight.
This time we shall start at the basics and next time we shall work our way into more complex topics. Since carbon is so essential and important, this will be a multipart series. I expect three or so, but that depends on how motivated I am to root around for things that will be interested.
Unlike beryllium and boron, carbon, at least 12C, is more common than it should be. The reason is fascinating, and we shall talk about that tonight.
Carbon has an atomic number (Z), the number of protons in the nucleus of 6. Carbon has 16 known isotopes with mass numbers ranging from eight to 22, inclusive. That means that the number of neutrons in the isotopes ranges from two to 16. Of those 16 isotopes, four are very important.
11C is artificially produced by bombarding 14N with protons. That material produces 15O which decays by emitting an alpha particle to 11C. It has a half life of just over 20 minutes, so it must be produced just before use. It has the interesting property of emitting positrons. Some very fast chemistry is done to the isotope to make it bind selectively to human tissue, and then it is injected into a medical patient for the process called Positron Emission Tomography, or the famous PET scan. It turns out that positrons are truly a form of antimatter, and when they encounter their normal matter counterpart, electrons, they annihilate each other, converting all of the mass of both particles to energy in the form of gamma rays, and sensitive detectors are used to image the region of the body under investigation. Hello, Star Trek!
By far the most common isotope of carbon is 12C, both cosmically and terrestrially. It is unusually common, and there a reason for that. In stars it is formed by a rare three body collision, (actually not quite, but almost) betwixt three alpha particles, just helium atoms stripped of both electrons. What actually happens is that two alphas collide and fuse into a 8 beryllium nucleus. This is unstable, with a half life of around 7 E-17 seconds. In stars like our sun, there is not enough flux of alphas to collide with the this material before it decays back to two alphas, but in older stars that have exhausted their hydrogen supply, the probability increases. However, that is not the entire story.
It turns out that there is a phenomenon called resonance that greatly increases the probability of a particular reaction occurring. You can visualize resonance by thinking of pushing a child in a swing. There are frequencies that depend on the mass of the child plus the swing seat and the length of the chain that can be increased with little energy input (pushing the child) and larger arcs that the swing makes. If you are out of sync, it takes a lot more push on your part to make the swing go higher, but if you are in the sweet spot, just a little more energy every push makes the swing go higher. It is a delicate balance.
Nuclei work like that, too. It turns out that there is a resonant state for 8Be and 12C, where the probability of the Be to capture a third alpha is high. Those are called vertical transitions, where the energy surfaces (a mathematical model of behavior) of the Be and the alpha “overlap” (very loosely used) with the 12C, making this transition highly facile when it does occur. With a high alpha flux and resonance, the probability of forming 12C is very high. This is why there is so much 12C in the universe. This is also called the triple alpha process, but it is not a true three body process. It is close, but remember that 7 E-17 half life: all three particles do not have to collide exactly at the same time. As I recall, 16O is way too common for similar reasons.
I looked for a long time for an explanation as to how 13C is formed. I drew a blank, so I shall speculate. Most folks think that 12C has a zero
neutron cross section, but that is not quite true. It does have a small cross section, and my speculation is that 13C is formed from 12C that happens to absorb a neutron here and there in stars. I have looked at other possible stellar nucleosynthetic routes, and none of them seem viable. It is possible that this isotope is a decay product from other elements, but that does not seem likely either. If any nuclear scientists are reading this, please clarify the origin of 13C.
13C is very cool because that nucleus has a nuclear spin that is -1/2. This has made possible wonderful advances in structural organic chemistry, because 1/2 spin nuclei give really nice and simple nuclear magnetic resonance (NMR) spectra. Even at only around 1.1% natural abundance, this has turned out to be an extremely powerful tool for the elucidation of molecular structures of millions of organic compounds.
NMR works by placing a sample in a strong, homogeneous magnetic field and then exposing it to radiofrequency quanta. Nuclei with a zero spin never absorb the radiofrequency quanta, but nuclei with a finite spin do. Those with spin of +/-1/2 give nice, sharp signals because they can align either with of against the direction of the magnetic field, so there is only a single transition available. Those with spins of greater than 1/2 (other allowed values are 1, 3/2, 2, etc.) have more complex spectra because they can align in more than two configurations in the field. 12C has a spin of zero, so it does not react because it does not align with the field at all. This is sort of a disadvantage since 13C is only 1.1% natural abundance, but with modern data acquisition equipment that can be overcome.
As an aside, ordinary hydrogen has a spin of +1/2 and is over 99.9% natural abundance, so before carbon NMR became available it was the most often used nucleus for analysis. That works out pretty well, because there are hydrogens in most organic compounds. But the very term “organic” requires that carbon be present, so it is very helpful to be able to do carbon NMR. It turns out that deuterium, 2H, (usually going by the symbol D) also has a zero spin, and these lacks of spin are exploited in NMR by using solvents that contain deuterium and 12C, such as chloroform-d, that have no NMR activity. Thus, a seeming disadvantage is turned into a boon.
Fundamentally, NMR works by causing the nucleus of interest to go from the lower energy state (either aligned parallel or antiparallel with the external field, depending of whether the 1/2 spin is plus or minus) to the other, slightly higher energy state. Every time that happens, a radiofrequency quantum is absorbed, and with trillions of transitions the diminution of radio signal can be detected.
The actual frequency that causes a transition is a function of the magnetic field AND of the electronic environment of the nucleus. The magnetic field is generally held constant (it has to be in superconducting NMR instruments) and the frequency of the radiofrequency energy is swept. (This is not strictly true in the most advanced instruments, but the concept is still valid). When the frequency is found where a transition occurs, some energy is absorbed. With experience with known compounds, databases have been accumulated that indicate around what frequency different chemical environments cause the transitions to occur.
This is closely related to magnetic resonance imaging (MRI), but differs in that the specific frequency for a transition is not as important as the time for a hydrogen nucleus to drop back down to the lower energy state. This relaxation time differs greatly depending on the chemical environment, and is used to derive images. Relaxation time if often the bane of the NMR analyst because if it is long, the signal fades and the rf energy has to be turned off to allow equilibrium to be reached, making analyses take more time than they would otherwise.
But it gets even better! Although all isotopes of any element, including carbon, undergo the exact same chemical reactions (the chemistry of an element is governed by the atomic number), the difference in mass betwixt isotopes more often than not make the rates of chemical reactions different. This has very wide reaching and important implications. I shall just tease you with that now, and for the very curious, you can look at this to whet your appetite.
The heaviest isotope of carbon of any value is 14C. It is not very common, but is extremely important. It exists in stars, but on earth is almost exclusively formed by cosmic rays. It turns out that cosmic rays are for the most part highly energetic hydrogen nuclei (protons) that come from the solar wind of stars. Those are just very energetic particles “boilt” off from chromospheres of stars. This isotope is formed by neutron absorption by half of a molecule of 14N2, which becomes 15 and immediately decomposes into an atom of 14N and an atom of 14C. The carbon atom immediately combines with oxygen in the atmosphere to form 14CO2 which is ultimately taken up by plants during photosynthesis.
14C transforms by beta decay to the stable 14N with a half life of a little over 5700 years. The importance of this isotope is in dating organic specimens, such as wood, cloth, bones, and the like. It turns out that the level of 14C in a given substance reaches a steady, known level as long as the material is living. After death, plants no longer absorb carbon dioxide and animals no longer eat the plant material that contains the sugars, starches, or cellulose containing 14C, so the amount begins to decline as it decays. By taking small (a few milligrams) samples and burning them, then doing some rather complex chemistry, the radiation and hence the concentration of 14C can be determined. Since the rate of decay of this isotope is known, the age of a specimen can be determined. Since so much of it has decayed in samples older than around 60,000 years, that is about the limit of age determination because there is just not enough signal to measure with any degree of precision.
This dating method, though generally reliable, has some difficulties. First, there is an assumption that 14C has been produced at a constant rate for the past 60,000 years. This is probably not quite true, because variations in solar output affects the flux of protons entering the atmosphere. This limitation can be overcome to some degree by using objects of known age (tree rings are excellent for this, but only go back so far) to correct for the variations of 14C levels. Another limitation is the assumption that the concentration of the isotope are similar globally, probably not as large of a limitation as the first one.
One factor that decreases the accuracy of dating fairly recent samples using this method is the use of fossil fuels since the Industrial Revolution. Those fuels are so ancient that all of the 14C has decayed, thus the carbon dioxide produced, when it goes into the atmosphere, dilutes the already tiny (only about a part per trillion) 14CO2 concentration. This can be corrected for, but complicates the issue. Another problem arose around 1950 during the Cold War when everyone was foolishly conducting atmospheric nuclear tests. The intense neutron release from those tests just about doubled the level of 14CO2 in the atmosphere, peaking in late 1963 in the northern hemisphere and in early 1965 for the southern hemisphere. Levels are now still about 20% higher than before the tests, but gradually are approaching historical baseline.
As I said previously, there are many other isotopes of carbon, but are either too short lived to be useful or are of theoretical importance only. Next time we shall examine the various types of pure carbon and later on will look into the chemistry of carbon with other elements. You would be surprised at how versatile carbon is, both as pure materials and in the huge variety of compounds that if forms.
Well, you have done it again! You have wasted many more einsteins of perfectly good photons reading this sooty piece. And even though Mitt Romney realizes that he was actually still running Bain in 2002 when he reads me say it, I always learn much more than I could possibly hope to teach by writing this series, so please keep those comments, questions, corrections, and other feedback coming. Tips and recs are also always very much appreciated.
I shall stay around this evening as long as comments warrant, but there is a large chance that I will get a late start because I have a feeling that I shall be visiting someone tonight. I shall return tomorrow evening for Review Time as well.
Warmest regards,
Doc, aka Dr. David W. Smith
Crossposted at
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the element of life?
Warmest regards,
Doc