Isotopes of Carbon

One of the fundamental ideas of nuclear physics is the isotope. In the 4th edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I describe isotopes at the start of Chapter 17.

Each atom contains a nucleus about 100,000 times smaller than the atom. The nuclear charge determines the number of electrons in the neutral atom and hence its chemical properties. The nuclear mass determines the mass of the atom. For a given nuclear charge there can be a number of nuclei with different masses or isotopes. If an isotope is unstable, it transforms into another nucleus through radioactive decay.

In order to understand isotopes, consider the isotopes of carbon, one of the most important elements for life.

¹²C

The most abundant isotope of carbon is ¹²C. This isotope is stable represents 99% of all carbon. The nucleus of ¹²C contains six protons (carbon’s atomic number is six) and six neutrons. The nucleus is basically three alpha particles stuck together.

¹³C

A second stable isotope is ¹³C, which contains six protons and seven neutrons. Only about 1% of carbon is ¹³C. The ratio of ¹³C to ¹²C is used to study ancient climates and oceans. Plants preferentially take up ¹²C, so the ¹³C/¹²C ratio provides a way to determine the amount of photosynthesis production, and contains information about the origin of carbon dioxide emission (to learn more, click here)

¹⁴C

All isotopes of carbon except ¹²C and ¹³C are unstable. The longest-lived unstable isotope is ¹⁴C, with a half-life of 5730 years. As with most isotopes containing an overabundance of neutrons, it decays by β^- emission (a neutron turns into a proton, with the emission of an electron). In Chapter 16 of IPMB, we describe how the decay of ¹⁴C contributes to the background radiation.

We are continuously exposed to radiation from natural sources. These include cosmic radiation, which varies with altitude and latitude; rock, sand, brick, and concrete containing varying amounts of radioactive minerals; the naturally occurring radionuclides in our bodies such as ¹⁴C and ⁴⁰K; and radioactive progeny from radon gas from the earth.

A homework problem in Chapter 17 describes how ¹⁴C is used to determine the age of organic remains.

Problem 58 One way to determine the age of biological remains is “carbon-14 dating.” The common isotope of carbon is stable ¹²C. The rare isotope ¹⁴C decays with a half-life of 5,370 yr. ¹⁴C is constantly created in the atmosphere by cosmic rays. The equilibrium between production and decay results in about 1 of every 10¹² atoms of carbon in the atmosphere being ¹⁴C, mostly as part of a CO₂ molecule. As long as the organism is alive, the ratio of ¹²C to ¹⁴C in the body is the same as in the atmosphere. Once the organism dies, it no longer incorporates ¹⁴C from the atmosphere, and the number of ¹⁴C nuclei begins to decrease. Suppose the remains of an organism have one ¹⁴C for every 10^{13 12}C nuclei. How long has it been since the organism died?

¹⁵C

Isotopes of carbon with even more neutrons can be created in the lab, but they have very short half-lives. For instance, ¹⁵C has a half-life of only 2.4 seconds

¹¹C

Isotopes that have fewer neutrons that found in the stable form often decay by  β⁺ emission, also known as positron decay. A proton transforms into a neutron, with the emission of a positron (an anti-electron). These nuclei can also decay by electron capture (an electron is captured by the nucleus, where it combines with a proton to produce a neutron), however most light elements such as carbon preferentially undergo β⁺ decay rather than electron capture. ¹¹C has a half-life of 20 minutes, and decays by positron emission. It is sometimes used for PET imaging, described in Chapter 17 of IPMB.

If a positron emitter is used as the radionuclide, the positron comes to rest and annihilates an electron, emitting two annihilation photons back to back. In positron emission tomography (PET) these are detected in coincidence. This simplifies the attenuation correction, because the total attenuation for both photons is the same for all points of emission along each γ ray through the body (see Problem 54). Positron emitters are short-lived, and it is necessary to have a cyclotron for producing them in or near the hospital.

Many PET applications use ¹¹C-acetate or ¹¹C-choline, which is administered to the patient. Imaging where the ¹¹C decays provides information about where carbon uptake occurs.

¹⁰C

Lighter isotopes of carbon, such as ¹⁰C, decay quickly; the half-life of ¹⁰C is 19 seconds. Such short half-lives make these isotopes difficult to use in PET imaging, even thought they are positron emitters.


By discussing the isotopes of carbon, we survey many of the most important ideas of nuclear physics, particularly those relevant to nuclear medicine.