21.3 Radioactive decay  (Page 5/21)

Because each nuclide has a specific number of nucleons, a particular balance of repulsion and attraction, and its own degree of stability, the half-lives of radioactive nuclides vary widely. For example: the half-life of ${}_{83}^{209}\text{Bi}$ is 1.9 $\times$ 10 ¹⁹ years; ${}_{94}^{239}\text{Ra}$ is 24,000 years; ${}_{86}^{222}\text{Rn}$ is 3.82 days; and element-111 (Rg for roentgenium) is 1.5 $\times$ 10 ^–3 seconds. The half-lives of a number of radioactive isotopes important to medicine are shown in [link] , and others are listed in Appendix M .

Radiometric dating

Several radioisotopes have half-lives and other properties that make them useful for purposes of “dating” the origin of objects such as archaeological artifacts, formerly living organisms, or geological formations. This process is radiometric dating    and has been responsible for many breakthrough scientific discoveries about the geological history of the earth, the evolution of life, and the history of human civilization. We will explore some of the most common types of radioactive dating and how the particular isotopes work for each type.

Radioactive dating using carbon-14

The radioactivity of carbon-14 provides a method for dating objects that were a part of a living organism. This method of radiometric dating, which is also called radiocarbon dating    or carbon-14 dating, is accurate for dating carbon-containing substances that are up to about 30,000 years old, and can provide reasonably accurate dates up to a maximum of about 50,000 years old.

Naturally occurring carbon consists of three isotopes: ${}_6^{12}\text{C}\text{,}$ which constitutes about 99% of the carbon on earth; ${}_6^{13}\text{C}\text{,}$ about 1% of the total; and trace amounts of ${}_6^{14}\text{C}.$ Carbon-14 forms in the upper atmosphere by the reaction of nitrogen atoms with neutrons from cosmic rays in space:

All isotopes of carbon react with oxygen to produce CO ₂ molecules. The ratio of ${}_6^{14}\text{C}{\text{O}}_2$ to ${}_6^{12}\text{C}{\text{O}}_2$ depends on the ratio of ${}_6^{14}\text{C}\text{O}$ to ${}_6^{12}\text{C}\text{O}$ in the atmosphere. The natural abundance of ${}_6^{14}\text{C}\text{O}$ in the atmosphere is approximately 1 part per trillion; until recently, this has generally been constant over time, as seen is gas samples found trapped in ice. The incorporation of ${}_6^{14}\text{C}{}_6^{14}\text{C}{\text{O}}_2$ and ${}_6^{12}\text{C}{\text{O}}_2$ into plants is a regular part of the photosynthesis process, which means that the ${}_6^{14}\text{C}\text{:}{}_6^{12}\text{C}$ ratio found in a living plant is the same as the ${}_6^{14}\text{C}\text{:}{}_6^{12}\text{C}$ ratio in the atmosphere. But when the plant dies, it no longer traps carbon through photosynthesis. Because ${}_6^{12}\text{C}$ is a stable isotope and does not undergo radioactive decay, its concentration in the plant does not change. However, carbon-14 decays by β emission with a half-life of 5730 years: