Most materials decay radioactively to some extent, but the decay rates of most are so long that, for all practical purposes, they can be considered inert. The remainder are said to be radioactive. Radioactive materials can decay in any of several ways, emitting either a particle or radiation and changing to a different element or isotope. The decay rate of radioactive materials does not depend on temperature, chemical environment, or similar factors. For dating purposes, the important parameter is the half-life of the reaction - the time it takes for half the material to decay. Half lives of various isotopes vary from microseconds to billions of years. Materials useful for radiometric dating have half lives from a few thousand to a few billion years.
Some types of radiometric dating assume that the initial proportions of a radioactive substance and its decay product are known. The decay product should not be a small-molecule gas that can leak out, and must itself have a long enough half life that it will be present in significant amounts. In addition, the initial element and the decay product should not be produced or depleted in significant amounts by other reactions. The procedures used to isolate and analyze the reaction products must be straightforward and reliable.
In contrast to most systems, isochron dating using rubidium-strontium does not require knowledge of the initial proportions.
Several systems are known that satisfy these constraints including carbon-14-carbon-12, Rb-Sr, Sm-Nd, K-Ar, Ar-Ar, and U-Pb. Carbon-14 has a fairly short half life and is used for dating recent organic remains. It is useful for periods up to perhaps 60,000 years and is thus very important to historians and archeologists as a method of determining the age of human artifacts. The other isotopes have half lives of hundreds of millions of years and are used for dating igneous rock formations.
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2 Example application 3 Related Articles |
The formula for the nuclei N remaining at time t is
Starting with
Starting with
1. Compute the decay constant for carbon-14 (in seconds for simplification)
Formulae related to radioactive decay
Nuclei N remaining at time t
Where N is number of nuclei remaining from the initial N0 sample after time t has elapsed, and λ is the decay constant. (See exponential decay).
Decay constant
Where λ is the decay constant in the reciprocal of the units of the half-life.
Derivation
Given a half-life h, after said half-life there will be half of the original amount remaining, so the formula can be changed to:
The decay constant can be solved for using algebraic manipulation.
Decay rate at time t
Where R is the radioactivity in nuclei per units of time (SI unit: Bq) after time t has elapsed and R0 is the initial radioactivity.
Derivation
If t = 0
Substitute:
Example application
Assume Carbon-14 decays by beta particle emission to Nitrogen-14 with a half-life of 5730 years a constant ratio of carbon-14 to carbon-12 is 1.3 x 10-12 (see Radiocarbon_dating).
Solution
2. Compute the number of carbon nuclei in a 25 gram sample (the gram molecular weight of carbon is 12.011 grams per mole).
3. Compute the initial activity of a carbon sample
4. Compute the elapsed time using the two computed decay rates.Related Articles