Earth's age

Humans have tried to determine the age of Earth for thousands of years by various means. Only when a clock-like mechanism, such as tree rings, relating the present day to some past time was discovered, could a reasonably accurate determination of Earth's age be made.

and Absolute Age

Determining the age of a material requires that there be some feature usable as a clock to count time backward from the present. The best and most familiar example of such a natural clock is the annual growth rings of trees. Counting the rings provides the absolute age of the tree because definite starting points and ending points exist for counting the number of years that have passed since the tree began to grow. The natural transmutation of certain radionuclides during millions of years permits the determination of the absolute age of rocks by providing the clock mechanism that ties the present day to a past starting point in time.

The structure of atoms consists primarily of three basic particles in a specific structural arrangement. These particles are the negatively charged electron, the positively charged proton, and the electrically neutral neutron. The protons and neutrons together form a small dense nucleus that is surrounded by a diffuse cloud of electrons. An equal number of electrons and protons also must exist to maintain electrical neutrality. Each element may contain atoms that have the same number of protons but different numbers of neutrons. Such atoms are known as isotopes, or nuclides.

Some nuclides are unstable and undergo fission processes that eject parts of the nuclear structure. Such processes alter the elemental identity of the particular atom by changing the number of protons in the nucleus. In each case, the decay of a naturally occurring nuclide produces atoms of a stable element.

Natural Transmutation

The symbols for the elements of the periodic table follow a strict international convention that unequivocally identifies the particular atom and specifies the isotopic form, or nuclide. According to this convention, the atomic number of the element (the number of protons in the nucleus) is shown as a preceding subscript and the atomic mass of the specific nuclide is shown as a preceding superscript. This can be confusing because the manner in which the element and nuclide weight are identified in normal speech is to state the name of the element and then the nuclide mass. Thus, to identify the particular nuclide of uranium having a mass of 238 units, one would write ²³⁸U but would pronounce the same as U-238 or uranium-238. When writing the equations of nuclear transmutation processes, including the nuclide mass is essential.

There are two main mechanisms by which an atom of one radionuclide transforms into an atom of a different nuclide. In one mechanism, a neutron in an unstable nucleus may decompose into a proton with the elimination of a β (beta) particle. The β particle is ejected as an electron. This is the mechanism whereby the isotope of carbon known as ¹⁴C transmutes to the corresponding nuclide of nitrogen, ¹⁴N. In the process, the nucleus of the ¹⁴C atom changes from the combination of six protons and eight neutrons to the combination of seven protons and seven neutrons. The ejected electron does not just disappear; it is quickly captured as energy by surrounding atoms. Although the elemental identity of the atom changes, its mass is not affected.

The other major mechanism of nuclear transmutation is through the ejection of an α (alpha) particle. The α particle is identical to the nucleus, of a helium atom, consisting of two protons and two neutrons. Ejection of an α particle from a nucleus, therefore, changes the elemental identity of the atom by two places in the periodic table and reduces the atomic mass by four units. Transmutation by the ejection of α particles is a process reserved for large atoms such as uranium, and the process can take place as a cascade in which the product nucleus that is immediately formed may itself eject an α particle and continue to do so until a stable atomic nucleus is formed. For example, the transmutation of uranium-238 (²³⁸U) to lead-206 (²⁰⁶Pb) occurs by this sequential process. The intermediate fission steps are unimportant, however, because they occur at a faster rate than the initial fission of ²³⁸U and so do not affect the half-life of the process.

Half-Life

Radionuclides undergo fission at an exponential rate described by the mathematical equation A = Aoe−kt, where A is the amount of material at time t, Ao is the amount at time t = 0, and k is the rate constant for the process. A special relationship exists for any time at which the quantity A is exactly one-half of the quantity Ao. The value of t is constant for all values of A and Ao for which this condition is true, and is referred to as the half-life of the process. Accordingly, it takes exactly the same amount of time for one million kilograms (kg) of a specific radionuclide to decay to one half-million kg as it does for one gram (g) to decay to one-half g.

The value of this relationship in regard to radiometric dating and the age of the earth is that it ties a past starting point to the present time and so acts as the clock necessary for counting time backward. Suppose that a mass of rock containing one kg of ²³⁸U was produced in the crust of the earth at some point in time. After one half-life has passed from that point in time, only one-half kg of ²³⁸U remains. After a second half-life has passed, one-half of that one-half kg, or one-quarter of kg, remains. After a third half-life has passed, another half of the existing ²³⁸U, or one-eighth of the original amount, remains. The process continues with the amount remaining each time being given by the equation A = Ao(1/2n), where n is the number of half-lives that have elapsed. In this way, knowing the amount of material present, and relating it to the amount of product nuclide, permits the calculation with reasonable certainty of the number of half-lives that have passed, and hence the age, of the material.

The length of a half-life for different processes covers an exceedingly broad range. Tables found in the CRC Handbook of Chemistry and Physics and other reference books list known half-lives for different radionuclides ranging from 10⁻¹⁶ seconds to more than 10⁹ years. In the majority of cases, the radionuclide sequence is not amenable to use as a timekeeping mechanism in radiometric dating. Measurement of the process may be problematic because of the actual duration of the half-life or because of the presence of materials that interfere with the analysis; these factors make uncertain the starting conditions of the source material.

The principal technique of determining nuclide ratios is through accurate mass analysis using mass spectrometry. A mass spectrometer functions using precise mathematical relationships that describe the circular trajectory of an ion having a certain mass and electrical charge as it travels through a magnetic field.

A typical mass spectrometric analysis begins by extracting the desired nuclide species from the matrix of interest. A sample of the extract is introduced into the injection port of the spectrometer, where it is given an electrical charge and directed into the magnetic field sector of the machine. Precise manipulation of the field strength directs ions to a detector in order according to mass. The detection circuitry counts the number of ions detected per unit time, and the results are displayed graphically and numerically. From the measured data, the relative proportions of nuclides and molecular fragments are determined, and the resulting values are used with the exponential rate equations to determine the number of half-lives that have passed for the process; from this one can determine the age of the material from which the nuclides were extracted.

Radiometric Age of Earth

Radiometric dating is a precise calculation because of the unequivocal structure of the atoms involved. Careful analysis of uranium ore such as pitchblende (U₃O₈) reveals the presence of a small amount of lead as the ²⁰⁶Pb nuclide, but no other lead isotopes. In lead ores that do not contain uranium, this isotope accounts for only 26 percent of the lead present. The stable ²⁰⁶Pb nuclide results only from the breakdown of ²³⁸U through a complex series of intermediate steps having much shorter half-lives. The initial fission step that is actually measured is the decay of ²³⁸U to the thorium radionuclide ²³⁴Th by ejection of an α particle, with a measured half-life of 4.6 billion years.

The subsequent steps of the process resulting in ²⁰⁶Pb are well known. The ²³⁴Th ejects a β particle to produce ²³⁴Pa (half-life = 24.1 days), which subsequently ejects another β particle to produce the uranium isotope ²³⁴U (half-life = 1.14 minutes). In β particle emission, the atomic number of the element increases by one unit while the atomic mass remains the same, but in α particle emission the atomic number decreases by two units and the atomic mass decreases by four units. Once formed, the ²³⁴U undergoes five successive α particle emissions to produce ²³⁰Th (half-life = 2.7 × 10⁵ years), ²²⁶Ra (half-life = 8.3 × 10⁴ years), ²²²Rn (half-life = 1.6 × 10³ years), ²¹⁸Po (half-life = 3.8 days), and ²¹⁴Pb (half-life = 3.1 minutes). This radionuclide of lead emits two successive β particles to produce first ²¹⁴Bi (half-life = 27 minutes) and then ²¹⁴Po (half-life = 20 minutes). The ²¹⁴Po emits an α particle to produce the ²¹⁰Pb radionuclide (half-life = 1.5 × 10⁻⁴ seconds), then ²¹⁰Bi (half-life = 22 years) and ²¹⁰Po (half-life = 5 days) by two successive β particle emissions. A final α particle emission transmutes the ²¹⁰Po into the stable nuclide ²⁰⁶Pb (half-life = 140 days). The specificity of the process is apparent, and no other known natural radionuclide decay process results in the formation of ²⁰⁶Pb.

Thus, assuming that no ²⁰⁶Pb existed in the pitchblende ore when it was initially formed, all of the ²⁰⁶Pb present in the ore originated through the series of transmutations just described. The assumption is verified by the observation that lead ores that do not contain uranium also do not contain ²⁰⁶Pb. Of the four stable isotopes of lead, only ²⁰⁴Pb is not produced through the transmutations of radionuclides. The ratio of ²⁰⁴Pb to ²⁰⁶Pb determines the amount of the latter nuclide present in excess of its natural abundance. The combination of these determinations from the examination of samples of ancient rock formations has indicated their age to be about 5 billion years. Analysis of other uranium-containing minerals provides a similar result.

Other radionuclide decay processes are known and have been used as a cross-check of Earth's age as determined by the ²³⁸U−²⁰⁶Pb process. The rubidium radionuclide ⁸⁷Rb transmutes to the stable strontium isotope ⁸⁷Sr with a half-life of 46 billion years, providing a much longer time frame in which to measure the age of the planet. Determinations based on this transformation have produced almost identical results for the age of Earth and for several meteorites that have been studied. Similarly, the decay of the potassium radionuclide ⁴⁰K to the inert and stable ⁴⁰Ar nuclide of argon (half-life = 1.3 × 10⁹ years) has also yielded similar results.

Errors

As with any empirical method of analysis, precision and accuracy of radiometric dating techniques are restricted by practical limitations. In any quantitative scientific determination, the value of the variable being measured can only be known within the limits of the least accurate measurement. The error limits of a technique determine the range of values within which the actual value may be found. For example, when volumes are measured using a standard titration burette, each reading has an error limit of, generally, 0.01 milliliter (mL). Errors from multiple readings accumulate in such a way that a volume determined by difference can be known only within 0.02 mL. This translates throughout subsequent calculations to the final range of values that necessarily includes the actual value of the quantity being determined.

The same logic applies in radiometric determinations such that only an approximate range of ages can be determined. Given that a determination may have a total error of ± 1 percent based on the limitations of the actual material manipulations involved in the laboratory, subsequent determination of the age can also be calculated only to the same error limit of ± 1 percent. Over the span of 4.6 × 10⁹ years, an age could thus be determined only as being within a span of 4.6 × 10⁷ years. Ages determined radiometrically are, therefore, generally stated for the midpoint of the range. Accordingly, many estimates of age determined by radiometric means are often called into question for verification by more precise measurements and techniques.

A source of error that becomes increasingly important as the length of time increases is the alteration of composition by the impingement of cosmic rays on Earth. Cosmic rays consist of a variety of high-energy particles, including protons, electrons, neutrons, x-rays, and α particles. The interaction of these, and especially of neutrons, with terrestrial nuclides brings about transmutations at a rate that increases the uncertainty of authentic nuclide counts as the time span increases. While this effect is most pronounced for ¹⁴C or radiocarbon dating, it also plays a role in increasing the uncertainty or error associated with other radionuclide transmutations.

Historical Estimates

Before the discovery of radioactivity in 1895 and before the more recent realization of precise measurement techniques by mass spectrometry, people attempted to determine the age of Earth by different means. Biblical scholars and Creation fundamentalists, even in the present day, relied on the tabulation of generations in the Bible to arrive at an absolute date for the formation of Earth. By their calculation, the planet could not be any more than about six thousand years old (having been formed, they figure, at 9:00 A.M. on October 23 in the year 4004 B.C.E.).

More scientific minds, however, have looked at natural phenomena, including erosion rates of soil and rock formations, the rate of deposit of sediments, and calculation of the time that would be required to achieve the level of salinity observed in the world's oceans. Such methods lack the clockwork mechanism that was provided by the exponential decay rate of radionuclide transmutations, and universally proved unsatisfactory as methods to determine the age of Earth.

Principal Terms

activity: the number of transmutations that occur in a specific process in a specific period of time, such as counts per minute

alpha (α) particle: the equivalent of the nucleus of a helium atom consisting of two protons and two neutrons ejected from the nucleus of some radionuclides as the mechanism of radioactive decay

beta (β) particle: a particle produced by the decomposition of a neutron to a proton, emitted from a nucleus as an electron during radioactive decay processes

electron capture: retention of the electron emitted from the nucleus as a β particle to balance the positive charge of the newly formed proton and maintain electrical neutrality of the nuclide atom

half-life: the length of time required for one-half of a given quantity of a radionuclide to decay to another nuclide in an exponential decay process

isotope: atoms of an element having the same number of protons but different numbers of neutrons in the nucleus

radionuclide: a radioactive isotope of an element

rate-determining step: the step in a multistep process that determines the maximum rate at which the overall change is observed to take place

transmutation: the conversion of an atom of one element into a corresponding atom of another element by altering the number of protons and neutrons within the nucleus

Bibliography

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"How Did Scientists Calculate the Age of Earth?" National Geographic, 19 Oct. 2023, education.nationalgeographic.org/resource/how-did-scientists-calculate-age-earth/. Accessed 10 Feb. 2025.

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