Want access to quizzes, flashcards, highlights, and more?
Access the full feature set for this content in a self-guided course!
Watching this resources will notify you when proposed changes or new versions are created so you can keep track of improvements that have been made.
Favoriting this resource allows you to save it in the “My Resources” tab of your account. There, you can easily access this resource later when you’re ready to customize it or assign it to your students.
Want access to quizzes, flashcards, highlights, and more?
Access the full feature set for this content in a self-guided course!
Want access to quizzes, flashcards, highlights, and more?
Access the full feature set for this content in a self-guided course!
The half-life of a radionuclide is the time taken for half the radionuclide's atoms to decay.
Explain what is a half-life of a radionuclide.
the time required for half of the nuclei in a sample of a specific isotope to undergo radioactive decay
A radionuclide is an atom with an unstable nucleus, characterized by excess energy available to be imparted either to a newly created radiation particle within the nucleus or via internal conversion.
The half-life of a radionuclide is the time taken for half of the radionuclide's atoms to decay. Taking
The half-life is related to the decay constant by substituting the condition
A half-life must not be thought of as the time required for exactly half of the atoms to decay.
The following figure shows a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not exactly one-half of the atoms remaining; there are only approximately one-half left because of the random variation in the process. However, with more atoms (the boxes on the right), the overall decay is smoother and less random-looking than with fewer atoms (the boxes on the left), in accordance with the law of large numbers.
A simulation of many identical atoms undergoing radioactive decay, starting with four atoms (left) and 400 atoms (right). The number at the top indicates how many half-lives have elapsed
The relationship between the half-life and the decay constant shows that highly radioactive substances are quickly spent while those that radiate weakly endure longer. Half-lives of known radionuclides vary widely, from more than 10^{19} years, such as for the very nearly stable nuclide 209 Bi, to 10^{−23} seconds for highly unstable ones.
The factor of ln(2) in the above equations results from the fact that the concept of "half-life" is merely a way of selecting a different base other than the natural base e for the lifetime expression. The time constant τ is the e^{-1}-life, the time until only 1/e remains -- about 36.8 percent, rather than the 50 percent in the half-life of a radionuclide. Therefore, τ is longer than t_{1/2}. The following equation can be shown to be valid:
Since radioactive decay is exponential with a constant probability, each process could just as easily be described with a different constant time period that (for example) gave its 1/3-life (how long until only 1/3 is left), or its 1/10-life (how long until only 1/10 is left), and so on. Therefore, the choice of τ and t_{1/2} for marker-times is only for convenience and for the sake of uploading convention. These marker-times reflect a fundamental principle only in that they show that the same proportion of a given radioactive substance will decay over any time period you choose.
Mathematically, the nth life for the above situation would be found by the same process shown above -- by setting
Boundless vets and curates high-quality, openly licensed content from around the Internet. This particular resource used the following sources: