Clocks in the Rocks

The following radioactive decay processes have proven particularly useful in radioactive dating for geologic processes:

Lead isochrons are also an important radioactive dating process.

Note that uranium-238 and uranium-235 give rise to two of the natural radioactive series, but rubidium-87 and potassium-40 do not give rise to series. They each stop with a single daughter product which is stable. Some of the decays which are useful for dating, with their half-lives and decay constants are:

* Note that ⁴⁰K also decays to ⁴⁰Ca with a decay constant of 4.962 x 10^-10yr^-1, but that decay is not used for dating. The half-life is for the parent isotope and so includes both decays.

Some decays with shorter half-lives are also useful. Of these, the ¹⁴C is unique and used in carbon dating. Note that the decay constant scale in the table below was kept the same as the table above for comparison.

Dalrymple's summary of isotopes is that there are 339 isotopes of 84 elements found in nature. Of those isotopes, 269 are stable and 70 are radioactive. Eighteen of the radioactive elements have long enough half-lives to have survived since the beginning of the solar system. The table above includes the main isotopes used for age studies.

Uranium-Lead Dating

Ages determined by radioactive decay are always subject to assumptions about original concentrations of the isotopes. The natural radioactive series which involve lead as a daughter element do offer a mechanism to test the assumptions. Common lead contains a mixture of four isotopes. Lead 204, which is not produced by radioactive decay provides a measure of what was "original" lead. It is observed that for most minerals, the proportions of the lead isotopes is very nearly constant, so the lead-204 can be used to project the original quantities of lead-206 and lead-207. (Lead-208 is the final stable product of the Thorium series, so is not used in uranium-lead dating.) The two uranium-lead dates obtained from U-235 and U-238 have different half-lives, so if the date obtained from the two decays are in agreement, this adds confidence to the date. They are not always the same, so some uncertainties arise in these processes.

There are powerful rationales for using lead isotopes as indicative of concentrations at the point when the lead-containing mineral was in the molten state. Since the isotopes of lead are chemically identical, any processes that brought lead into the mineral would be completely indiscriminate about which isotope was brought in. The forming mineral will incorporate lead-204, lead-206 and lead-207 at the ratio at which they are found at that location at the time of formation. Any departure from the original relative concentrations of lead-206 and lead-207 relative to lead-204 could then be attributed to radioactive decay.

Making use of the decay constants of both ²³⁸U and ²³⁵U, plus the fact that the consistent isotopic ratio of ²³⁸U/²³⁵U = 137.88 is found, Holmes and Houtermans developed a system to use the ratios of the lead isotopes to produce Pb-Pb isochrons for dating minerals. This approach is generally considered to be the most precise for determining the age of the Earth.

Uranium-Lead dating has been used in the Grand Canyon to date two layers of deep formations in what is called the Grand Canyon Supergroup. In a set of layers called the Unkar Group there is an upper layer of basaltic lava called the Cardenas Lavas which has been dated at 1104 +/- 2 Myr. A lower layer named the Bass Formation has a layer of volcanic ash at its base which has been dated at 1255 +/-2 Myr.

Potassium-Argon Method

Potassium-Argon dating has the advantage that the argon is an inert gas that does not react chemically and would not be expected to be included in the solidification of a rock, so any found inside a rock is very likely the result of radioactive decay of potassium. Since the argon will escape if the rock is melted, the dates obtained are to the last molten time for the rock. The radioactive transition which produces the argon is electron capture.

One thing to note about K/Ar dating is that it will never give an overestimate of the age, so it is a good tool for determining lower bounds.

Rubidium-Strontium Isochrons

The rubidium-strontium pair is often used for dating and has a non-radiogenic isotope, strontium-86, which can be used as a check on original concentrations of the isotopes. This process is often used along with potassium-argon dating on the same rocks. The ratios of rubidium-87 and strontium-87 to the strontium-86 found in different parts of a rock sample can be plotted against each other in a graph called an isochron which should be a straight line. The slope of the line gives the measured age. The oldest ages obtained from the Rb/Sr method can be taken as one indicator of the age of the earth.

The isotope ⁸⁷Rb decays into the ground state of ⁸⁷Sr with a half-life of 4.88 x 10¹⁰ years and a maximum β^- energy of 272 keV.

Rubidium-Strontium

The rubidium-strontium dating method is often used in geologic studies.

This is a rubidium-strontium isochron for a set of samples of a Precambrian granite body exposed near Sudbury, Ontario. The data is from T. E. Krogh, et al., Carnegie Institute Washington Year Book, Vol 66, 1968, p. 530.

Age of the Earth

To the intriguing question "How old is the Earth?" we can of course only provide models and model calculations based on the best data we can get. While there are numerous natural processes that can serve as clocks, there are also many natural processes that can reset or scramble these time-dependent processes and introduce uncertainties. To try to set a reasonable bound on the age, we could presume that the Earth formed at the same time as the rest of the solar system. If the small masses that become meteorites are part of that system, then a measurement of the solidification time of those meteorites gives an estimate of the age of the Earth. The following illustration points to a scenario for developing such an age estimate.

Some of the progress in finding very old samples of rock on the Earth are summarized in the following comments.

"The oldest rocks on earth that have been dated thus far include 3.4 billion year old granites from the Barberton Mountain Land of South Africa, 3.7 billion year old granites of southwestern Greenland, ..." Levin, 1983

But later in 1983: "Geologists working in the mountains of western Australia have discovered grains of rock that are 4.1 to 4.2 billion years old, by far the oldest ever found on the Earth" This dating was done on grains of zircon, a mineral so stable that it can retain its identity through volcanic activity, weathering, and sedimentation. It is a compound of zirconium, silicon and oxygen which in its colorless form is used to make brilliant gems. Samples more than 3.5 billion years old have been found in eight or more locations, including Wisconsin, Minnesota, South Africa, Greenland, and Labrador.

Older ages in the neighborhood of 4.5 billion years are obtained from meteoritic samples. The graph below follows the treatment of Krane of Rb-Sr studies of meteorite samples from Wetherill in order to show the nature of the calculation of age from isochrons.

Show calculation

If you had 100% pure parent element when you began a dating process, then radioactive dating would be extremely reliable since the radioactive half-life of a given isotope is quite independent of any natural forces save direct collision-type interactions with the nucleus. Considering the relative scale of nuclei and atoms, nuclei are so remote from the outer edge of the atoms that no environmental factors affect them. However, there are two obvious problems with radioactive dating for geological purposes: 1) uncertainty about the composition of the original sample and 2) possible losses of material during the time span of the decay.

The rubidium/strontium dating method deals with both of those difficulties by using the non-radioactive isotope strontium-86 as a comparison standard. The relative amounts of strontium-87 and -86 are determined with great precision and the fact that the data fits a straight line is a strong argument that none of the constituents was lost from the mix during the aging process.

The 4.5 billion year age for the earth is consistent with the results of the potassium/argon and uranium/lead processes. Similar results are also obtained from the study of spontaneous fission events from uranium-238 and plutonium-244.

One of the standard references for modeling the age of the Earth is G. Brent Dalrymple, The Age of the Earth, Stanford University Press, 1991.

Meteorite Dating

"Meteorites, which many consider to be remnants of a disrupted planet that oriaginally formed at about the same time as the earth, have provided uranium-lead and rubidium-strontium ages of about 4.6 billion years. From such data, and from estimates of how long it would take to produce the quantities of various lead isotopes now found on the earth, geochronologists feel that the 4.6-billion-year age for the earth can be accepted with confidence." Levin

Moon Rock Dating

The ages of rocks returned to Earth from the Apollo missions range from 3.3 to about 4.6 billion years. The older age determinations are derived from rocks collected on the lunar highland, which may represent the original lunar crust.

Age of the Moon

Our best clues to the age of the Moon are the radiometric dates of the oldest Moon rocks, those from the lunar highlands. Dalrymple reports that thirteen samples from the lunar highlands gave the oldest ages. These were collected by Apollo 15, 16, 17 and Luna 20. The radiometric dates range from 3.9 to 4.5 Gy. If we take the oldest ages to be the age of the Moon, then we place that age at about 4.5 Gy.

A sample of the kind of data that leads to such a projected age is the rubidium-strontium isochron of lunar sample 72417 which yields a time to last melting of 4.47 Gy. This isochron was discussed in Dalrymple and credited to Papanastassiou and Wassenburg, 1975.

Lunar sample 72417

This lunar sample was collected on the Apollo 17 lunar mission. It's largest mineral constituent is olivine and the actual form is called dunite.

Sample 72417 was one of five chips from this half-meter boulder in found at Station 2 at the base of South Massif. The boulder is described as a metaclastic breccia, and the specific sample location was described as part of a clast of dunite. The boulder showed signs of deformation and crushing by impacts with some shock-induced melting and recrystallization. Even with all these complications, the Rb-Sr isochron is impressive evidence that the samples used for the isochron came out of the melt at about the same time.

Source boulder for #72417

Lunar sample 72417

The sample is about 3cm long, so this view is about 3x actual size.

Online references:
Catalog entry for sample 72417
Lunar Sample 72417
Wiki on Dunite