HalfLife of Radioactive Decay
The halflife is a parameter for the rate of decay that is related to the decay constant by:
Learning Objective

Calculate the halflife of a radioactive element
Key Points
 The relationship between time, halflife, and the amount of radionuclide is defined by:
$N={N}_{0}{e}^{\lambda t}$ .  The relationship between the halflife and the decay constant shows that highly radioactive substances rapidly transform to daughter nuclides, while those that radiate weakly take longer to transform.
 Since the probability of a decay event is constant, scientists can describe the decay process as a constant time period.
Term

halflife
The time required for half of the nuclei in a sample of a specific isotope to undergo radioactive decay.
Full Text
Decay Rates
Radioactive decay is a random process at the singleatom level; is impossible to predict exactly when a particular atom will decay. However, the chance that a given atom will decay is constant over time. For a large number of atoms, the decay rate for the collection as a whole can be computed from the measured decay constants of the nuclides, or, equivalently, from the halflives.
Radioactive decay simulation
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 halflives have elapsed
Given a sample of a particular radionuclide, the halflife is the time taken for half of its atoms to decay. The following equation is used to predict the number of atoms (N) of a a given radioactive sample that remain after a given time (t):
In this equation, λ, pronounced "lambda," is the decay constant, which is the inverse of the mean lifetime, and N_{0} is the value of N at t=0. The equation indicates that the decay constant λ has units of t^{1}_{.}
The halflife is related to the decay constant. If you set N =
This relationship between the halflife and the decay constant shows that highly radioactive substances are quickly spent, while those that radiate weakly endure longer. Halflives vary widely; the halflife of ^{209}Bi is 1019 years, while unstable nuclides can have halflives that have been measured as short as 10^{−23} seconds.
Example
What is the halflife of element X if it takes 36 days to decay from 50 grams to 12.5 grams?
50 grams to 25 grams is one halflife.
25 grams to 12.5 grams is another halflife.
So, for 50 grams to decay to 12.5 grams, two halflives, which would take 36 days total, would need to pass. This means each halflife for element X is 18 days.
Key Term Reference
 atom
 Appears in these related concepts: Overview of Atomic Structure, Description of the Hydrogen Atom, and Stable Isotopes
 decay
 Appears in these related concepts: Radioactive Decay Series: Introduction, Models Using Differential Equations, and Discovery of Radioactivity
 element
 Appears in these related concepts: Development of the Periodic Table, Elements and Compounds, and The Periodic Table
 nuclide
 Appears in these related concepts: Dating Using Radioactive Decay, Nuclear Stability, and Rate of Radioactive Decay
 period
 Appears in these related concepts: Frequency of Sound Waves, Sine and Cosine as Functions, and Tangent as a Function
 probability
 Appears in these related concepts: Theoretical Probability, Rules of Probability for Mendelian Inheritance, and The Addition Rule
 radioactive decay
 Appears in these related concepts: Alpha Decay, Nuclear Stability, and Tracers
 substance
 Appears in these related concepts: Substances and Mixtures, Types of Synthetic Organic Polymers, and Complex Ion Equilibria and Solubility
 unstable
 Appears in these related concepts: The Bohr Model, Isotopes, and Irreversible Addition Reactions
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