The correct answer is: Carbon-14.
Carbon-14 dating is a radiometric dating method that uses the naturally occurring radioisotope carbon-14 (14C) to estimate the age of carbon-bearing materials up to about 58,000 to 62,000 years old. Carbon-14 is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. It is one of the three naturally occurring isotopes of carbon, along with 12C and 13C. Carbon-14 is produced in the upper atmosphere by cosmic rays striking nitrogen atoms, which convert them to 14C. 14C is then incorporated into plant and animal tissues through photosynthesis and respiration. When an organism dies, it stops exchanging carbon with its environment and the amount of 14C in its tissues begins to decay. The decay of 14C is a first-order process, meaning that the amount of 14C in a sample decreases exponentially over time. The half-life of 14C is 5,730 years, which means that half of the 14C in a sample will decay in 5,730 years.
Carbon-14 dating is used to date a wide variety of materials, including wood, bone, charcoal, and plant remains. It is also used to date archaeological artifacts, such as pottery and stone tools. Carbon-14 dating is a very accurate method of dating, and it has been used to date some of the oldest objects in the world.
The other options are incorrect because they are not used for dating very old objects of archaeological importance. Phosphorus-31 is a stable isotope of phosphorus that is not radioactive. Tritium is a radioactive isotope of hydrogen with an atomic nucleus containing 1 proton and 2 neutrons. Radium is a radioactive element with the symbol Ra and atomic number 88. It is a member of the alkaline earth metals and is chemically similar to barium and strontium. Radium is a highly radioactive element and is used in nuclear power plants and medical imaging.