Determining Absolute Age of Fossils

The goal of this lesson is to understand the methods of absolute dating.

Absolute age is determined primarily by radioactive methods. Radioactive dating involves collecting data of the radioactive sources and researching time life of the element. Radioactive elements emit particles and energy as they break down. The radioactive half-life, the time it take for a given radioisotope to lose half of its life, is not affected by temperature, physical or chemical state, or any other influence of the environment outside the nucleus. So, radioactive samples continue to decay at a predictable rate. If reasonable estimates of the original composition of a radioactive sample can be made, then the amounts of the radioisotopes present can provide a measurement of the time elapsed.

One such method is called carbon dating, which is limited to the dating of organic (once living) materials. The longer-lived radioisotopes in minerals provide evidence of long time scales in geological processes. While original compositions cannot be determined with certainty, various combination measurements provide consistent values for the times of formations of certain geologic deposits. Most absolute dating is done by measuring the amount of radioactive isotopes such as Carbon 14 or Uranium left in a rock or a fossil.

As soon as a living organism dies, it stops taking in new carbon. The ratio of carbon-12 to carbon-14 at the moment of death is the same as every other living thing, but the carbon-14 decays and is not replaced. The carbon-14 decays with its half-life of 5,700 years, while the amount of carbon-12 remains constant in the sample. By looking at the ratio of carbon-12 to carbon-14 in the sample and comparing it to the ratio in a living organism, it is possible to determine the age of a formerly living thing fairly precisely.

A formula to calculate how old a sample is by carbon-14 dating is:

t = [ ln (Nf/No) / (-0.693) ] x t1/2

ln is the natural logarithm

Nf/No is the percent of carbon-14 in the sample compared to the amount in living tissue t1/2 is the half-life of carbon-14 (5,700 years).

Compute the following with percentages.

8, 20, 4, and 16.

So, if you had a fossil that had 10 percent carbon-14 compared to a living sample, then that fossil would be:

t = [ ln (0.10) / (-0.693) ] x 5,700 years

t = [ (-2.303) / (-0.693) ] x 5,700 years

t = [ 3.323 ] x 5,700 years

t = 18,940 years old

Because the half-life of carbon-14 is 5,700 years, it is only reliable for dating objects up to about 60,000 years old. However, the principle of carbon-14 dating applies to other isotopes as well.

Another useful radioisotopes for radioactive dating include Uranium -235 (half-life = 704 million years), Uranium -238 (half-life = 4.5 billion years), Thorium-232 (half-life = 14 billion years) and Rubidium-87 (half-life = 49 billion years. Summary of Uranium Isotopes

Isotope Number Number Half-Life

of Protons of Neutrons in Years

Uranium-238 92 146 4.46 billion

Uranium-235 92 143 704 million

Uranium-234 92 142 245,000

Uranium-238, the most prevalent isotope in uranium ore and has a half-life of about 4.5 billion years. That means half the atoms in any sample will decay in that amount of time. The various decay products, referred to as progeny or daughters, form a decay chain starting at uranium-238 and ending with the stable isotope lead-206. The nuclei of radioactive elements are unstable, meaning they are transformed into other elements, typically by emitting particles. Radioactive decay generally results in the emission of alpha or beta particles from the nucleus. It is often also accompanied by emission of gamma radiation.

Uranium Decay Chain

Isotope	Half Life	Decays by
Uranium-238	4.46 billion years	alpha
Thorium-234	24.1 days	Beta
Protactinium-234m	1.17 minutes	Beta
Uranium-234	245,000 years	Alpha
Thorium-230	75,400 years	Alpha
Radium-226	1,600 years	Alpha
Radon-222	3.82 days	Alpha
Polonium-218	3.11 minutes	Alpha
Lead-214	26.8 minutes	Beta
Bismuth-214	19.9 minutes	Beta
Polonium-214	163 microseconds	Alpha
Lead-210	22.3 years	Beta
Bismuth-210	5.01 days	beta
Polonium-210	138 days	Alpha

↓

Lead 2o6 Stable

Absolute Dating

Take the presented information and deduce the age by using the Carbon 14 formula.

A formula to calculate how old a sample is by carbon-14 dating is:

t = [ ln (Nf/No) / (-0.693) ] x t1/2

ln is the natural logarithm

Nf/No is the percent of carbon-14 in the sample compared to the amount in living tissue t1/2 is the half-life of carbon-14 (5,700 years).

Compute the following with percentages.

1. 8

2. 20

3. 4

4. 16

Using the same percentages listed, use the formula to estimate fossils with Uranium 238 emission. Remember the half life is 4.5 billion years.