Half life carbon dating calculations of drug

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During natural radioactive decay, not all atoms of an element are instantaneously changed to atoms of another element. The decay process takes time and there is value in being able to express the rate at which a process occurs. Half-lives can be calculated from measurements on the change in mass of a nuclide and the time it takes to occur. The only thing we know is that in the time of that substance's half-life, half of the original nuclei will disintegrate.
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Nuclear Half-Life Calculations

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Half-Lives and Radioactive Decay Kinetics

Another approach to describing reaction rates is based on the time required for the concentration of a reactant to decrease to one-half its initial value. This period of time is called the half-life The period of time it takes for the concentration of a reactant to decrease to one-half its initial value. If two reactions have the same order, the faster reaction will have a shorter half-life, and the slower reaction will have a longer half-life. The half-life of a first-order reaction under a given set of reaction conditions is a constant. This is not true for zeroth- and second-order reactions. The half-life of a first-order reaction is independent of the concentration of the reactants. This becomes evident when we rearrange the integrated rate law for a first-order reaction Equation
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5.7: Calculating Half-Life

Nuclear half-life expresses the time required for half of a sample to undergo radioactive decay. Exponential decay can be expressed mathematically like this:. So, if a problem asks you to calculate an element's half-life, it must provide information about the initial mass, the quantity left after radioactive decay, and the time it took that sample to reach its post-decay value.
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The atoms of radioactive substances have unstable nuclei that emit alpha, beta and gamma radiation to achieve a more stable configuration. When an atom undergoes radioactive decay, it can transform into a different element or into a different isotope of the same element. For any given sample, the decay doesn't occur all at once, but over a period of time characteristic of the substance in question.