You are watching: The half life of carbon 14 is 5730 years

When we speak the the facet Carbon, we most frequently refer to the most naturally plentiful stable isotope 12C. Return 12C is absolutely essential to life, its stormy sister isotope 14C has come to be of excessive importance come the scientific research world. Radiocarbon date is the procedure of determining the age of a sample by analyzing the amount of 14C remaining against its known half-life, 5,730 years. The reason this process works is since when organisms room alive, they space constantly replenishing your 14C supply through respiration, providing them with a constant amount the the isotope. However, once an organism end to exist, that no much longer takes in carbon indigenous its environment and the turbulent 14C isotope begins to decay. From this science, we are able to almost right the date at i m sorry the organism live on Earth. Radiocarbon dating is offered in numerous fields to learn information about the past problems of organisms and also the environments existing on Earth.

## The Carbon-14 Cycle

Radiocarbon date (usually advert to just as carbon-14 dating) is a radiometric date method. It provides the naturally arising radioisotope carbon-14 (14C) to calculation the age of carbon-bearing materials up to about 58,000 to 62,000 year old. Carbon has actually two stable, nonradioactive isotopes: carbon-12 (12C) and carbon-13 (13C). There are also trace amounts of the turbulent radioisotope carbon-14 (14C) top top Earth. Carbon-14 has a reasonably short half-life of 5,730 years, definition that the fraction of carbon-14 in a sample is halved over the food of 5,730 years due to radioactive degeneration to nitrogen-14. The carbon-14 isotope would certainly vanish indigenous Earth"s atmosphere in less than a million years to be it no for the consistent influx the cosmic rays communicating with molecules of nitrogen (N2) and solitary nitrogen atom (N) in the stratosphere. Both processes of formation and decay the carbon-14 are shown in number 1.

Figure 1: diagram of the formation of carbon-14 (forward), the degeneration of carbon-14 (reverse). Carbon-14 is constantly created in the atmosphere and cycled through the carbon and nitrogen cycles. As soon as an organism is de-coupled from these cycles (i.e., death), climate the carbon-14 decays till there is basically none left.When plants fix atmospheric carbon dioxide (CO2) into organic compounds during photosynthesis, the resulting fraction of the isotope 14C in the plant organization will match the portion of the isotope in the atmosphere (and biosphere because they are coupled). ~ a plantdies, the organization of every carbon isotopes, consisting of 14C, stops and the concentration that 14C declines due come the radioactive degeneration of 14C following.

< ce ^14C -> ^14N + e^- + mu_e labelE2>

This adheres to first-order kinetics:

where

(N_0) is the variety of atoms the the isotope in the original sample (at time t = 0, once the organism from which the sample is obtained was de-coupled indigenous the biosphere). (N_t) is the variety of atoms left after ~ time (t). (k) is the rate consistent for the radiation decay.The half-life the a radiation isotope (usually denoted through (t_1/2)) is a more familiar ide than (k) because that radioactivity, for this reason although Equation (
efE3) is express in regards to (k), that is much more usual come quote the value of (t_1/2). The right now accepted value for the half-life that 14C is 5,730 years. This means that after ~ 5,730 years, only fifty percent of the early stage 14C will certainly remain; a quarter will remain after 11,460 years; an eighth after ~ 17,190 years; and so on.

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The equation relating rate continuous to half-life for first order kinetics is

< k = dfracln 2 t_1/2 labelE4>

so the rate constant is then

< k = dfracln 25.73 imes 10^3 = 1.21 imes 10^-4 extyear^-1 labelE5>

and Equation ( efE2) have the right to be rewritten as

or

The sample is suspect to have actually originally had the exact same 14C/12C proportion as the ratio in the atmosphere, and since the size of the sample is known, the total number of atoms in the sample deserve to be calculated, yielding (N_0), the variety of 14C atoms in the original sample. Measurement of N, the variety of 14C atoms right now in the sample, allows the calculate of (t), the age of the sample, utilizing the Equation ( efE7).