Lesson 31A: Using Radioactive Decay to Determine Geologic Age

Estimated Time: One forty-five minute class period

Indicator(s) Core Learning Goal 1:

1.1.2 The student will modify or affirm scientific ideas according to accumulated evidence.

1.2.7 The student will use relationships discovered in the lab to explain phenomena observed outside the laboratory.

1.4.1 The student will organize data appropriately using techniques such as tables, graphs, and webs (for graphs: axes labeled with appropriate quantities, appropriate units on axes, axes labeled with appropriate intervals, independent and dependent variables on correct axes, appropriate title).

1.4.4 The student will determine the relationships between quantities and develop the mathematical model that describes these relationships.

1.5.1 The student will demonstrate the ability to summarize data (measurements/observations).

Indicator(s) Core Learning Goal 2:

2.6.2 The student will research the change in the belief in the age of the earth.

At least — fossil record, rock layers, radioactive dating, Big Bang theory

Student Outcome(s):

The student will be able to explain how geologists use radioactive dating to determine the age of an Earth material by completing a simulation activity and analyzing data.

Brief Description:

Students will complete a short simulation of the radioactive decay of an element. They will record their data in a data chart then construct a graph of the data. You will need to teach your students how to draw a "best fit" line on a graph.

Background knowledge / teacher notes:

The full text the USGS publication titled, Geologic Time Online Edition is available online at http://pubs.usgs.gov/gip/geotime/.

In order to complete this activity:

  1. Have students work in pairs or small groups.
  2. Any small cube-shaped objects will suffice - sugar cubes, math cubes, homemade cubes of wood or Styrofoam, or dice.
  3. Students should already have been exposed to the concepts of relative time, absolute time, radioactivity and rates of radioactive decay.

At the close of the 18th century, the haze of fantasy and mysticism that tended to obscure the true nature of the Earth was being swept away. Careful studies by scientists showed that rocks had diverse origins. Some rock layers, containing clearly identifiable fossil remains of fish and other forms of aquatic animal and plant life, originally formed in the ocean. Other layers, consisting of sand grains winnowed clean by the pounding surf, obviously formed as beach deposits that marked the shorelines of ancient seas. Certain layers are in the form of sand bars and gravel banks — rock debris spread over the land by streams. Some rocks were once lava flows or beds of cinders and ash thrown out of ancient volcanoes; others are portions of large masses of once-molten rock that cooled very slowly far beneath the Earth's surface. Other rocks were so transformed by heat and pressure during the heaving and buckling of the Earth's crust in periods of mountain building that their original features were obliterated.

From the results of studies on the origins of the various kinds of rocks (petrology), coupled with studies of rock layering (stratigraphy) and the evolution of life (paleontology), today geologists reconstruct the sequence of events that has shaped the Earth's surface. Their studies show, for example, that during a particular episode the land surface was raised in one part of the world to form high plateaus and mountain ranges. After the uplift of the land, the forces of erosion attacked the highlands and the eroded rock debris was transported and redeposited in the lowlands. During the same interval of time in another part of the world, the land surface subsided and was covered by the seas. With the sinking of the land surface, sediments were deposited on the ocean floor. The evidence of the pre-existence of ancient mountain ranges lies in the nature of the eroded rock debris, and the evidence of the seas' former presence is, in part, the fossil forms of marine life that accumulated with the bottom sediments.

Such recurring events as mountain building and sea encroachment, of which the rocks themselves are records, comprise units of geologic time even though the actual dates of the events are unknown. By comparison, the history of mankind is similarly organized into relative units of time. We speak of human events as occurring either BC or AD, broad divisions of time. Shorter spans are measured by the dynasties of ancient Egypt or by the reigns of kings and queens in Europe. Geologists have done the same thing to geologic time by dividing the Earth's history into Eras, broad spans based on the general character of life that existed during these times, and Periods, shorter spans based partly on evidence of major disturbances of the Earth's crust.

The names used to designate the divisions of geologic time are a fascinating mixture of works that mark highlights in the historical development of geologic science over the past 200 years. Nearly every name signifies the acceptance of a new scientific concept, a new rung in the ladder of geologic knowledge.

The discovery of the natural radioactive decay of uranium in 1896 by Henry Becquerel, the French physicist, opened new vistas in science. In 1905, the British physicist, Lord Rutherford, after defining the structure of the atom, made the first clear suggestion for using radioactivity as a tool for measuring geologic time directly. Shortly thereafter, in 1907, Professor B. B. Boltwood, radiochemist of Yale University, published a list of geologic ages based on radioactivity. Although Boltwood’s ages have since been revised, they did show correctly that the duration of geologic time would be measured in terms of hundreds-to-thousands of millions of years.

The next 40 years was a period of expanding research on the nature and behavior of atoms, leading to the development of nuclear fission and fusion as energy sources. A byproduct of this atomic research has been the development and continuing refinement of the various methods and techniques used to measure the age of Earth materials. Precise dating has been accomplished since 1950.

A chemical element consists of atoms with a specific number of protons in their nuclei but different atomic weights owing to variations in the number of neutrons. Atoms of the same element with differing atomic weights are called isotopes. Radioactive decay is a spontaneous process in which an isotope (the parent) loses particles from its nucleus to form an isotope of a new element (the daughter). The rate of decay is conveniently expressed in terms of an isotope's half-life, or the time it takes for one-half of a particular radioactive isotope in a sample to decay. Most radioactive isotopes have rapid rates of decay (that is, short half-lives) and lose their radioactivity within a few days or years. Some isotopes, however, decay slowly, and several of these are used as geologic clocks. The parent isotopes and corresponding daughter products most commonly used to determine the ages of ancient rocks are listed below:

Parent Isotope Stable Daughter Product Currently Accepted Half-life Values

Uranium-238 Lead-206 4.5 billion years

Uranium-235 Lead-207 704 million years

Thorium-232 Lead-208 14.0 billion years

Rubidium-87 Strontium-87 48.8 billion years

Potassium-40 Argon-40 1.25 billion years

Samarium-147 Neodymium-143 106 billion years


The mathematical expression that relates radioactive decay to geologic time is called the age equation and is:

t =1/delta ln(1 + D/P)


t is the age of a rock or mineral specimen,

D is the number of atoms of a daughter product today,

P is the number of atoms of the parent product today,

ln is the natural logarithm (logarithm to base e), and

delta is the appropriate decay constant.

(The decay constant for each parent isotope is related to its half-life, t 1/2, by the following expression:

t 1/2 = ln2/delta

Dating rocks by these radioactive timekeepers is simple in theory, but the laboratory procedures are complex. The numbers of parent and daughter isotopes in each specimen are determined by various kinds of analytical methods. The principal difficulty lies in measuring precisely very small amounts of isotopes.

Literally thousands of dated materials are now available for use to bracket the various episodes in the history of the Earth within specific time zones. Many points on the time scale are being revised, however, as the behavior of isotopes in the Earth's crust is more clearly understood. Thus the graphic illustration of the geologic time scale, showing both relative time and radiometric time, represents only the present state of knowledge. Certainly, revisions and modifications will be forthcoming as research continues to improve our knowledge of Earth history.

Reprinted from: USGS. Background. Time and Change/ Using Radioactive Decay to Determine Geologic Age.

Lesson Description:


  1. Have one student use the chalkboard to list the names of everyone in her/his immediate family (parents, siblings) in order from the oldest to the youngest. Tell the student not to list the ages of any member.
  2. Ask the remainder of the class if there is any way to know from the available information the exact age of any member of the family. They will realize it is not possible. The information they have can only be used to determine relative age, i.e., father is older than son or daughter, etc.
  3. Explain that relative age is often used in the study of rocks. As scientists recognized that layers of rock had been deposited in sequence, one on top of another, they derived the principle of superposition, which says that in any sequence of strata, not later disturbed, the order in which they were deposited is from bottom to top. Therefore, rocks on the bottom of a sequence of undisturbed strata are older than rocks on the top of the sequence.
  4. Have students identify the type of information they would need to determine the absolute age of any family member.


Explain to students that they are going to participate in an activity that will demonstrate to them how geologists determine the absolute age of rocks or minerals.

Instructions to students:

  1. The cubes you have been given represent the imaginary chemical element "Dorkium".
  2. Place a mark (dot) on one side of all 100 cubes with a felt-tip pen and put the cubes in the box.
  3. Hold the lid on the box tightly. Gently turn the box over twice. Remove lid.
  4. Take out all cubes that have the marked-side up. These cubes represent atoms that have decayed into the daughter element DOD (Daughter of Dorkium). In the data table beside Trial 1, record the number of cubes removed and the number of cubes remaining.
  5. Repeat these procedures until you have completed twelve trials or until all the cubes have been removed.


  1. Have students use the data collected in the chart to construct a graph. On the vertical axis, plot the number of cubes remaining each time. On the horizontal axis, plot the trial numbers.
  2. Connect the points they have plotted. Draw a best-fit line for these points.

Journal Write:

  1. How does the graph illustrate the concept you have explored?.
  2. Explain what is meant by "radioactive decay of an element."
  3. How does half-life of a radioactive element relate to its decay?
  4. How can half-life be used as an "atomic clock."
  5. Differentiate between relative and absolute dating.


Explain that several real chemical elements are used as atomic clocks — Uranium 238, Carbon 14, Potassium 40, etc., and that each is useful for determining the ages of particular kinds of rocks or minerals of a given span of time, e.g., Carbon 14 can be used for relatively young rocks (generally less than 55,000 years), whereas Uranium 238 can be used for very old rocks or minerals (more than 1 billion years).

  1. Create a concept map to show how scientists might use the tool of radioactive dating to enhance our knowledge of Earth systems and subsystems.
  2. Why is radioactive dating a tool often associated with the biosphere?

Education Element:



Imagine the Universe Using Radioactive Decay to measure supernovae remnants



Journal Write: Describe how geologists use radioactive dating to determine the age of the Earth.


Shoe box with lid

100 cubes (sugar cubes work well)

Data table (included below)


USGS Learning Web. Time and Change/ Using Radioactive Decay to Determine Geologic Age. Available:


Prentice Hall (1999). The Earth System. Global change on long time scales.. pp. 10-12.


Dorkium Decay Data Chart


Trial Number

Number of

Daughter Atoms

Number of Dorkium

Atoms Remaining