Half-life (physics) The half-life of a substance is the time it takes for half of the substance to decay. The word "half-life" was first used when talking about radioactive elements where the number of atoms get smaller over time by changing into different atoms. It is now used in other situations, such as the time it takes for a drug in the body to be half gone. A Geiger-Muller detector can be used to measure the radioactive half-life; it is the time when the activity is half the original. Half-life depends on probability because the atoms decay at a random time. Half-life is the expected time when half the number of atoms have decayed, on average. Radioactive isotopes are atoms that have unstable nuclei, meaning that the nucleus of each atom will decay after enough time has passed. Their nuclei are unstable because the arrangement of protons and neutrons in them change. This is known as radioactive decay. When they decay, they release particles such as alpha particles, beta particles, gamma rays. Sometimes they decay by fission, which means to break into pieces, to make smaller nuclei. For example, a radioactive carbon-14 atom releases a beta particle to become nitrogen-14.

12C has six protons and six neutrons, for a mass number of twelve. All of the isotopes of carbon have the same number of protons; therefore, 13C has seven neutrons, and 14C has eight neutrons. The different isotopes of an element can also be indicated with the mass number hyphenated (for example, C-12 instead of 12C). Hydrogen has three common isotopes, shown in Figure 2.5. An isotope that contains more than the usual number of neutrons is referred to as a heavy isotope. An example is 14C. Heavy isotopes tend to be unstable, and unstable isotopes are radioactive. A radioactive isotope is an isotope whose nucleus readily decays, giving off subatomic particles and electromagnetic energy. Different radioactive isotopes (also called radioisotopes) differ in their half-life, the time it takes for half of any size sample of an isotope to decay. For example, the half-life of tritium—a radioisotope of hydrogen—is about 12 years, indicating it takes 12 years for half of the tritium nuclei in a sample to decay.

The time required for half the nuclei in a sample of an isotope to undergo radioactive decay.: #* #*

half-life. This refers to the time required for half of a given number of radioactive atoms to decay and is inversely related to the isotope's decay constant In nuclear science a decay chain refers to the predictable series of radioactive disintegrations undergone by the nuclei of certain unstable chemical elements. Radioactive isotopes do not usually decay directly to stable isotopes, but rather into another radioisotope. The isotope produced by this radioactive emission then decays into another, often radioactive isotope. This chain of decays always In nuclear science a decay chain refers to the predictable series of radioactive disintegrations undergone by the nuclei of certain unstable chemical elements. Radioactive isotopes do not usually decay directly to stable isotopes, but rather into another radioisotope. The isotope produced by this radioactive emission then decays into another, often radioactive isotope. This chain of decays always terminates in a stable isotope, whose nucleus no longer has the surplus of energy necessary to produce another emission of radiation. Such stable isotopes are then said to have reached their ground states. The stages or steps in a decay chain are referred to by their relationship to previous or subsequent stages. Hence, a parent isotope is one that undergoes decay to form a daughter isotope. For example element 92, uranium, has an isotope with 144 neutrons (236U) and it decays into an isotope of element 90, thorium, with 142 neutrons (232Th). The daughter isotope may be stable or it may itself decay to form another daughter isotope. 232Th does this when it decays into radium-228. The daughter of a daughter isotope, such as 228Ra, is sometimes called a granddaughter isotope. 228Ra in turn undergoes a further eight decays and transmutations until a stable isotope, 208Pb, is produced, terminating the decay chain of 236U. The time required for an atom of a parent isotope to decay into its daughter is fundamentally unpredictable and varies widely. For individual nuclei the process is not known to have determinable causes and the time at which it occurs is therefore completely random. The only prediction that can be made is statistical and expresses an average rate of decay. This rate can be represented by adjusting the curve of a decaying exponential distribution with a decay constant (λ) particular to the isotope. On this understanding the radioactive decay of an initial population of unstable atoms over time t follows the curve given by e−λt. One of the most important properties of any radioactive material follows from this analysis, its half-life. This refers to the time required for half of a given number of radioactive atoms to decay and is inversely related to the…