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The half-life \((T_{1/2})\) of a radioactive substance is defined as the time for half of the original nuclei to decay (or the time at which half of the original nuclei remain). The half-lives of unstable isotopes are shown in the chart of nuclides .
Half-Life Formula. The half-life of a radioactive substance, denoted by the symbol T 1/2, can be represented mathematically. If you start with a certain number of radioactive atoms, after one half-life, half of those atoms will have decayed.
The half-life of a reaction is the time required for the reactant concentration to decrease to one-half its initial value. The half-life of a first-order reaction is a constant that is related to the rate constant for the reaction: t 1/2 = 0.693/ k. Radioactive decay reactions are first-order reactions.
In a chemical reaction, the half-life of a species is the time it takes for the concentration of that substance to fall to half of its initial value. In a first-order reaction the half-life of the reactant is ln (2)/λ, where λ (also denoted as k) is the reaction rate constant.
Half-life \(t_{1/2}\) is the time in which there is a 50% chance that a nucleus will decay. The number of nuclei \(N\) as a function of time is \[N = N_0e^{-\lambda t},\] where \(N_0\) is the number present at \(t = 0\), and \(\lambda\) is the decay constant, related to the half-life by \[\lambda = \dfrac{0.693}{t_{1/2}}.\]
Calculate the age of a material based upon its half-life. Describe how carbon-14 is used to determine the age of carbon containing objects. Give examples of other isotopes used in radioactive dating. Appreciate the half-life of isotopes involved in nuclear weapons and reactors.
The half-life calculator is a tool that helps you understand the principles of radioactive decay. You can use it to not only learn how to calculate half-life, but also as a way of finding the initial and final quantity of a substance or its decay constant.
Each radioactive nuclide has a characteristic, constant half-life (t 1/2), the time required for half of the atoms in a sample to decay. An isotope’s half-life allows us to determine how long a sample of a useful isotope will be available, and how long a sample of an undesirable or dangerous isotope must be stored before it decays to a low ...
The radioactive half-life for a given radioisotope is a measure of the tendency of the nucleus to "decay" or "disintegrate" and as such is based purely upon that probability.
Basic Concepts. It is often energetically favorable for nuclei to undergo transmutation, either converting a proton to a neutron (or vice versa), emitting some combination of nucleons, or splitting apart. This is radioactive decay.