# Write an equation to represent the beta decay of carbon-14 decay

An element is defined by the number of protons in the atomic nucleus. For instance, a nucleus with just one proton is hydrogen, a nucleus with two protons is helium, and a nucleus with 92 protons is uranium, the heaviest naturally occurring element. The number of protons in an atomic nucleus determines the atomic number, Z. In an electrically neutral atom of atomic number Z, there will be Z protons and Z electrons. Bring fact-checked results to the top of your browser search. Principles of isotopic dating All absolute isotopic ages are based on radioactive decaya process whereby a specific atom or isotope is converted into another specific atom or isotope at a constant and known rate.

Most elements exist in different atomic forms that are identical in their chemical properties but differ in the number of neutral particles—i.

## Principles of isotopic dating

For a single element, these atoms are called isotopes. Because isotopes differ in mass, their relative abundance can be determined if the masses are separated in a mass spectrometer see below Use of mass spectrometers. Radioactive decay can be observed in the laboratory by either of two means: The particles given off during the decay process are part of a profound fundamental change in the nucleus.

To compensate for the loss of mass and energythe radioactive atom undergoes internal transformation and in most cases simply becomes an atom of a different chemical element.

In terms of the numbers of atoms present, it is as if apples changed spontaneously into oranges at a fixed and known rate. In this analogythe apples would represent radioactive, or parent, atoms, while the oranges would represent the atoms formed, the so-called daughters.

Pursuing this analogy further, one would expect that a new basket of apples would have no oranges but that an older one would have many. In fact, one would expect that the ratio of oranges to apples would change in a very specific way over the time elapsed, since the process continues until all the apples are converted.

In geochronology the situation is identical. A particular rock or mineral that contains a radioactive isotope or radio-isotope is analyzed to determine the number of parent and daughter isotopes present, whereby the time since that mineral or rock formed is calculated.

Of course, one must select geologic materials that contain elements with long half-lives—i. The age calculated is only as good as the existing knowledge of the decay rate and is valid only if this rate is constant over the time that elapsed. Fortunately for geochronology the study of radioactivity has been the subject of extensive theoretical and laboratory investigation by physicists for almost a century.

The results show that there is no known process that can alter the rate of radioactive decay. By way of explanation it can be noted that since the cause of the process lies deep within the atomic nucleus, external forces such as extreme heat and pressure have no effect.

The same is true regarding gravitational, magnetic, and electric fields, as well as the chemical state in which the atom resides.

In short, the process of radioactive decay is immutable under all known conditions. Although it is impossible to predict when a particular atom will change, given a sufficient number of atoms, the rate of their decay is found to be constant. The situation is analogous to the death rate among human populations insured by an insurance company. Even though it is impossible to predict when a given policyholder will die, the company can count on paying off a certain number of beneficiaries every month.

The recognition that the rate of decay of any radioactive parent atom is proportional to the number of atoms N of the parent remaining at any time gives rise to the following expression: Converting this proportion to an equation incorporates the additional observation that different radioisotopes have different disintegration rates even when the same number of atoms are observed undergoing decay.

Two alterations are generally made to equation 4 in order to obtain the form most useful for radiometric dating. In the first place, since the unknown term in radiometric dating is obviously t, it is desirable to rearrange equation 4 so that it is explicitly solved for t.

Half-life is defined as the time period that must elapse in order to halve the initial number of radioactive atoms.

## Evaluation and presentation schemes in dating

The half-life and the decay constant are inversely proportional because rapidly decaying radioisotopes have a high decay constant but a short half-life. With t made explicit and half-life introduced, equation 4 is converted to the following form, in which the symbols have the same meaning: Alternatively, because the number of daughter atoms is directly observed rather than N, which is the initial number of parent atoms present, another formulation may be more convenient.

Since the initial number of parent atoms present at time zero N0 must be the sum of the parent atoms remaining N and the daughter atoms present D, one can write: Substituting this in equation 6 gives If one chooses to use P to designate the parent atom, the expression assumes its familiar form: This follows because, as each parent atom loses its identity with time, it reappears as a daughter atom.

Equation 8 documents the simplicity of direct isotopic dating. The time of decay is proportional to the natural logarithm represented by ln of the ratio of D to P. In short, one need only measure the ratio of the number of radioactive parent and daughter atoms present, and the time elapsed since the mineral or rock formed can be calculated, provided of course that the decay rate is known.

Likewise, the conditions that must be met to make the calculated age precise and meaningful are in themselves simple:Here is a history of questions and answers processed by "Ask the Physicist!". If you like my answer, please consider making a donation to help support this service..

If there is a link to a previously answered question, be patient. grupobittia.com is the place to go to get the answers you need and to ask the questions you want. Written by Dr. Peter Kreeft. Dr. Peter Kreeft is a professor of philosophy at Boston College and a noted Catholic apologist and philosopher.

He is a convert to the Catholic Church from reformed Protestantism. The older a sample of a radioactive material, the less radioactive it is. The decrease in radioactivity follows a characteristic pattern shown in the graph or decay curve.. The y axis can represent the % radioisotope left OR the measured radioactivity.

The older a sample of a radioactive material, the less radioactive it is. The decrease in radioactivity follows a characteristic pattern shown in the graph or decay curve.. The y axis can represent the % radioisotope left OR the measured radioactivity. How radiometric dating works in general: Radioactive elements decay gradually into other elements.

The original element is called the parent, and the result of the decay process is called the daughter element.

Unreliability of Radiometric Dating and Old Age of the Earth