# Parent and daughter isotope relationship

### Absolute Geologic Time

When an isotope emits an alpha particle, the resultant daughter product has an atomic sample by evaluating the amount of parent and daughter isotopes in it. The decay of a radioactive substance follows an exponential relationship. Half-life - Parent Daughter Isotopes More Parent-Daughter Relationships . Finally, correlation between different isotopic dating methods may be required to . A daughter isotope is the product of a Parent isotope.

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.

## Decay product

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.

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: The rock or mineral must have remained closed to the addition or escape of parent and daughter atoms since the time that the rock or mineral system formed. It must be possible to correct for other atoms identical to daughter atoms already present when the rock or mineral formed.

The decay constant must be known. The measurement of the daughter-to-parent ratio must be accurate because uncertainty in this ratio contributes directly to uncertainty in the age. Different schemes have been developed to deal with the critical assumptions stated above. In uranium—lead datingminerals virtually free of initial lead can be isolated and corrections made for the trivial amounts present.

In whole rock isochron methods that make use of the rubidium—strontium or samarium—neodymium decay schemes see belowa series of rocks or minerals are chosen that can be assumed to have the same age and identical abundances of their initial isotopic ratios. The results are then tested for the internal consistency that can validate the assumptions. In all cases, it is the obligation of the investigator making the determinations to include enough tests to indicate that the absolute age quoted is valid within the limits stated.

For example, the age of the Amitsoq gneisses from western Greenland was determined to be 3. Accurate radiometric dating generally requires that the parent has a long enough half-life that it will be present in significant amounts at the time of measurement except as described below under "Dating with short-lived extinct radionuclides"the half-life of the parent is accurately known, and enough of the daughter product is produced to be accurately measured and distinguished from the initial amount of the daughter present in the material.

The procedures used to isolate and analyze the parent and daughter nuclides must be precise and accurate. This normally involves isotope ratio mass spectrometry. The precision of a dating method depends in part on the half-life of the radioactive isotope involved.

For instance, carbon has a half-life of 5, years. After an organism has been dead for 60, years, so little carbon is left that accurate dating can not be established. On the other hand, the concentration of carbon falls off so steeply that the age of relatively young remains can be determined precisely to within a few decades.

For example, decay of the parent isotope Rb Rubidium produces a stable daughter isotope, Sr Strontiumwhile releasing a beta particle an electron from the nucleus. Numerical ages have been added to the Geologic Time Scale since the advent of radioactive age-dating techniques. Many minerals contain radioactive isotopes. In theory, the age of any of these minerals can be determined by: It illustrates how the amount of a radioactive parent isotope decreases with time.

This amount is a percentage of the original parent amount.

### Isotopes and Radioactivity Tutorial

Time is expressed in half-lives. Experiment by dragging on the graph. Note that this half-life can be obtained from the graph at the point where the decay and growth curves cross. Determine the half-lives for the other three isotopes and enter your estimate into the text fields below each graph. Note the differences in scale between the various graphs Re-setting the Clock - Closure temperature If a material that selectively rejects the daughter nuclide is heated, any daughter nuclides that have been accumulated over time will be lost through diffusion, setting the isotopic "clock" to zero.

The temperature at which this happens is known as the closure temperature or blocking temperature and is specific to a particular material and isotopic system. These temperatures are experimentally determined in the lab by artificially resetting sample minerals using a high-temperature furnace. As the mineral cools, the crystal structure begins to form and diffusion of isotopes is less easy.

At a certain temperature, the crystal structure has formed sufficiently to prevent diffusion of isotopes. This temperature is what is known as closure temperature and represents the temperature below which the mineral is a closed system to isotopes.

Thus an igneous or metamorphic rock or melt, which is slowly cooling, does not begin to exhibit measurable radioactive decay until it cools below the closure temperature. The age that can be calculated by radiometric dating is thus the time at which the rock or mineral cooled to closure temperature.

This field is known as thermochronology or thermochronometry. Radiocarbon Dating The radiocarbon dating method was developed in the 's by Willard F. Libby and a team of scientists at the University of Chicago. It subsequently evolved into the most powerful method of dating late Pleistocene and Holocene artifacts and geologic events up to about 50, years in age.

The radiocarbon method is applied in many different scientific fields, including archeology, geology, oceanography, hydrology, atmospheric science, and paleoclimatology. Rubidium occurs in nature as two isotopes: Rb decays with a half-life of Which minerals and rocks can be dated with the Rb-Sr method?

## Decay chain

The minerals must contain Rb, which is a rather rare element. Examples include the mica family biotite and muscovite and the feldspar family plagioclase and orthoclase. Select a fresh, unweathered rock sample. Sample Selection A geologist collects a fresh, unweathered hand sample for age dating.

- What is a parent isotope? What is a daughter isotope?

Fresh is the key word here, and means that the chemistry of the sample has NOT been changed since the sample formed. Weathering alters the chemistry of rocks including their isotopic compositions. Therefore, a highly weathered rock may yield unreliable age information.

Crush the rock and separate the Rb-bearing minerals. Getting a Rock Sample Ready for the Mass Spectrometer For reliable age determination, careful sample preparation is an important and often tedious process. The rock is mechanically crushed into small fragments. Fragments of the Rb-bearing minerals are then separated from the whole rock using a variety of methods, such as a magnetic separator.

These materials are then used to prepare a "whole-rock" sample and several "mineral separate" samples.