Radioactive Decay, Half-Life, and Carbon Dating Help (page 2)

By — McGraw-Hill Professional
Updated on Aug 30, 2011


All radioactive isotopes have a specific set, half-life . These time periods are not dependent on pressure, temperature, or bonding properties.

The half-life of a radioactive isotope is the time needed for Geological Time Half-life of a specific element sample to decay.

For example, the half-life of 238 U 92 is 4.5 × 10 9 years. It is amazing to think that the uranium found today will be around for another four billion years.

In 1953, Clair Patterson and Friedrich Houtermans separately determined the age of the Earth and the solar system as being around 4.6 billion years old by finding and comparing the radioactive decay rates of isotopes of lead in the earliest rocks known to exist.

Through the radiometric dating of ancient rocks, the Earth was calculated to be over four billion years old. Zircon crystals found in Western Australia have radiometric ages of over 4.3 billion years.

By figuring out how long the oldest lead ores took to change from their earliest formation (nebular gas) to later compression and inclusion in the Earth’s crust, scientists were then able to estimate the age of lead-containing meteorites. These meteorites have been dated at nearly 4.6 million years using the radioactive decay of uranium-235 to lead-207.

In this same way, Patterson and Houtermans were able to estimate the age of our solar system to be about 4.54 billion years. The age of our Milky Way galaxy was judged to be between 11 and 13 billion years.

In a study published in Science in January 2003, a team of researchers estimated that the Universe was between 11.2 and 20 billion years old.

Most estimates of the Universe’s age, in recent years, have ranged between 10 and 15 billion years. Data supplied by the Hubble Space Telescope in 2003 led to a refined estimate of 13–14 billion years.

The new calculations, by Lawrence Krauss of Case Western Reserve University and Brian Chaboyer at Dartmouth College, involved new information about old star clusters in our galaxy and a better understanding of how stars evolve. It was based on when stars are thought to end the main sequence of their lives, a point at which they’ve used up the hydrogen that fuels thermonuclear fusion and therefore begin to dim.

Carbon Dating

Isotopes are also used in the dating of ancient soils, plants, animals, and the tools of early peoples. An isotope of carbon, 14 C, which has a half-life of 5730 years, can be used to calculate geological age. Since the radioactive decay rate of carbon is constant, observing its decay rate allows the measurement of the number of years that have past compared to carbon’s half-life.

The preservation of the original organic sample can affect carbon dating. Carbon-14, which decays to 14 N, is mostly used for dating samples of fairly recent geological age. Most scientists believe that carbon dating is only accurate for dating specimens thought to be between 30,000 and 50,000 years old. Carbon dating is particularly helpful when finding the age of bone, wood, shell, fossils, and other organic samples since they all contain carbon. These plants and animals use carbon in their basic structure and usually have a good amount of carbon left to be measured.

Other radiometric methods that make use of uranium, lead, potassium, and argon measure much longer time periods since they are not limited to the organic remains of prehistoric samples. Table 2-1 shows a few of the elements used to date samples of different ages.

Table 2-1 Isotopes used to date geological samples.

Isotopes (original)

Isotopes (decay products)

Half-life (years)

Dating accuracy (range in years)







4.8 billion

10 million–4.6 billion



1.3 billion

50,000–4.6 billion

  • ranium-238


4.5 billion

10 million–4.6 billion


Dating samples is not an exact science. A lot of factors have to be considered when a sample is dated, including its preservation and the amount of erosion and exposure it has suffered. For example, when lead is depleted from a rock sample through erosion, then the uranium used to date the sample through the breakdown of the uranium to the lead end product (daughter) would show an incorrectly young age.

Practice problems of this concept can be found at: Geological Time Practice Test

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