• Introduction
• Advance Preparation and Materials Needed
• Geology Learning Outcomes
• Methods
• Lab Procedures
• Absolute Ages from Ratios of Radioactive Isotopes and Daughter Products
• Measuring Geologic Ages Using Isotope Ratios and a Mathematical Formula
• Determining Relative Geologic Ages
• Applying Principles of Geologic Time to the Grand Canyon
• Table of the Geologic Time Scale (page will open in new window)

Introduction

There are two ways to think about the geologic age of something:

1. When it occurred relative to other events in a sequence, which is called its relative geologic age.
2. How many years ago it occurred, which is called its absolute geologic age.

Advance Prepration and Materials Needed

• Read this page completely. It is specifically designed to prepare you for completing the lab worksheet. The worksheet, which is separate, contains a different set of detailed questions that you will answer and turn in.
• Read the following Basics page: Geologic Time. It will help you become familiar with the role of stratigraphy in understanding geologic history, how principles of geologic age determination can be used to find the the relative age of geologic events, and how radiometric dating methods can provide absolute ages for certain geologic materials. In addition, the Geologic Time Basics page includes an introduction to the Geologic Time Scale and the age of the earth.
• To perform the lab you will need:
• a scientific calculator
• colored pencils
• the Geologic Time Lab Worksheet

Geology Learning Outcomes

By performing and completing this lab, you will progress toward the following learning objectives for this course:

• Think, behave, and communicate scientifically by writing paragraphs that make use of terminology for geologic ages and the principles used by geologists to determine geologic ages, and expressing geologic ages using large numbers and correct units.
• Gather, show, and explain evidence of the earth as a dynamic, ever-changing planet by sequencing, explaining and narrating the geologic history of the Grand Canyon.Put geologic events in order and determine the age of geologic materials by applying the principles of relative geologic age.
• Interpret spatial and quantitative information with maps and diagrams by applying principles of relative geologic age to a cross-section diagram of the Grand Canyon.
• Use measurements, numbers, calculations and graphs to derive meaning from the earth by measuring absolute geologic ages using ratios, a graph, and an exponential equation.
• Think, behave, and communicate scientifically.

Methods

• Construct or examine graphs to analyze correlations between types of data.
• Apply principles of relative geologic age.
• Calculate ages of earth materials.

Lab Procedures

There are three parts to this lab: working with graphs and calculations to derive absolute ages based on the decay of radioactive isotopes, practice using the principles of relative geologic to determine age sequences represented on cross-sections and block diagrams, and applying relative geologic age principles to the geology of the Grand Canyon.

Refer to the Lab Assignments Grading Rubric for a reminder of what constitutes a well-performed lab.

Part 1: Absolute Ages from Ratios of Radioactive Isotopes and Daughter Products

An isotope system is assumed to be a closed system with regard to the parent and daughter - they remain within the system and do not leave it, and at the same time no isotopes of the parent or daughter type enter the system from outside. (In reality, rocks, minerals and other geologic materials can be checked to see if the isotope system remained closed, rather than assuming so.)

At time zero, 100% of the isotopes are the parent isotopes. By the definition of a half-life, the amount of parent isotope at each half-life is half of what it was before the half-life elapsed.

As the amount of parent isotope decreases by radioactive decay, the amount of the daughter isotope increases commensurately. Therefore, at any time, the total of parent isotope fraction and daughter isotope fraction add up to 1. Similarly, the percentage of parent isotope percentage and daughter isotope percentage add up to 100 at all times.

The table below tracks the decay, half-life by half-life, of a radioactive isotope, and the accumulation of the daughter product isotope that the parent changes into once it decays. What numbers would go in the blanks?

Radioactive Isotope Decay in Half-Lives
Half-Lives Elapsed	Parent Isotope Fraction	Daughter Isotope Fraction	Parent Isotope Percent	Daughter Isotope Percent
0	1	0	100%	0%
1	1/2
2
3
4
5
6
7
8
9
10

Measuring Geologic Ages Using Isotope Ratios and a Mathematical Formula

There are several different radioactive isotope systems that are used for measuring ages of geologic materials. For more information on these systems, see the isotopes and half-lives section of the Geologic Time Basics page.

There is a definite mathematical relationship between the ratio of the amount of daughter product isotope to the amount of radioactive parent isotope, and the number of half-lives that have elapsed. The relationship is non-linear, involving a logarithmic function.

The mathematical formula can be used to determine exactly how much time has elapsed, for any fraction of parent/daughter isotope, without having to make a visual estimate from a graph. The mathematical formula is expressed as follows:

age = (half-life) x ln (D/P + 1) ÷ ln2

where age is the absolute age (typically using years as the time unit), ln is the natural logarithm, D is the amount of daughter isotope, and P is the amount of parent isotope. D/P is just the ratio of the amount of daughter product isotope to the amount of radioactive parent isotope. The half-life is a constant, a number, which depends on the isotope. For example, if the age is based on measurements of the amount of uranium-238 (²³⁸U) and the lead-206 (²⁰⁶Pb) that is its daughter product, the half-life value to use is 4,600,000,000 yr. (In English, that is four billion, six hundred million years. In scientific notation, the half-life of ²³⁸U is 4.6 X 10⁹ yr.

In the table below there are data from six different geological samples. The same isotope system is used for each pair of samples, but the daughter to parent ratio is different in each sample. How would you use these data to calculate the geologic age indicated by the isotopes in each sample?

Geologic Age Calculation
Sample #	Isotope system: Parent - Daughter	Half-Life (years)	Ratio of Daughter Isotope - Parent Isotope (D/P)
1	14C -- 14N carbon-14 to nitrogen-14	5,730	1.51
2	14C -- 14	5,730	2.48
3	40K -- 40Ar potassium-40 to argon-40	1,300 million	0.655
4	40K -- 40Ar	1,300 million	0.358
5	238U -- 206Pb uranium-238 to lead-206	4,500 million	0.296
6	238U -- 206Pb	4,500 million	0.015

Part 2. Determining Relative Geologic Ages

You can use principles of relative geologic age to determine sequences of geologic events, including rock formations, intervals of erosion, tilting, folding, and faulting like those represented in the block diagrams and cross-sections below. Be sure to review the principles of relative geologic age on the Geologic Time Basics page .

You can click on each of the images in Part 2 for a larger version in a separate browser window.

The figure above is a block diagram represents three horizontal geologic strata (layered formations of rock).

• Which stratum is the youngest?
• Which is the oldest?

• Which principle of relative geologic age did you use to determine the age sequence of the strata?

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The block diagram above shows five geologic strata. Assuming they have not been turned upside down, what is the age sequence of the strata?

• Which principle of relative geologic age tells us that the strata have been tilted?
• Which principle of relative geologic age did you use to determine the age sequence of the strata?

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The block diagram above shows geologic strata that have been arched into a type of fold called an anticline. What is the age sequence of the strata?

• Which principle of relative geologic age tells us that the strata have been folded?
• Which principle of relative geologic age did you use to determine the age sequence of the strata?

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The cross-section above shows three geologic strata, a layer of sandstone on top of a formation of conglomerate on top of a pluton. The pluton is made of the same type of granite that is in the pebble clasts of the conglomerate. The contact between the granite and the conglomerate is irregular, similar to how the present-day surface of the land is irregular.

• What is the age relationship of the three types of rock?
• Which principle of relative geologic age did you use to determine the age sequence of the strata?
• What type of unconformity is the contact between the granite and the conglomerate?
• What must have happened in the time between when the granite intruded and solidified, and the conglomeratic sediment was deposited?

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The cross-section above shows four types of rock in relationship to each other: granite, shale, sandstone and, along the contact of the shale with the granite, hornfels.

• What is the age relationship of the different types of rock in the cross-section?
• Which principle of relative geologic age allows you to deduce whether the sandstone is younger than the shale?
• Which principle of relative geologic age allows you to deduce whether the granite is younger than the shale?
• What is the age relationship of the granite and hornfels?

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The block diagram above shows four sedimentary rock formations, a dike of igneous rock, and a fault.

• What is the age relationship of the bodies of rock and the fault in the block diagram?
• Which principle of relative geologic age allows you to deduce whether the fault is older younger than the dike?

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The cross-section above shows nine rock formations and two unconformities.

• What is the age relationship of the different rock types, the two unconformities, and the tilting?
• What are the two types of unconformities?

Part 3. Applying Principles of Geologic Time to the Grand Canyon

The diagram below is a simplified representation of the stratigraphy of the Grand Canyon. When you go to Grand Canyon National Park in Arizona and hike down the Kaibab Trail, from the South Rim to the Colorado River, a mile below, you will pass through these formations of rock. Consistent with the principle of superposition, the deeper in the Canyon you go, the older the rocks are. For study purposes, some parts of the Grand Canyon stratigraphy are not shown in the diagram. The Precambrian strata have been reduced to a representative set of formations. The Paleozoic strata do not include the Temple Butte Limestone and Surprise Canyon Formation, which are not widespread in the Grand Canyon. Some formations of rock younger than Paleozoic, also not widespread in Grand Canyon, are not included here.

Study the figure and notice the unconformities. There is a major nonconformity, a major angular unconformity and a major disconformity. Where are they?

Below is a stratigraphic sequence for the the Grand Canyon in the form of a table. Each geologic formation in the sequence is briefly described. This is the type information that geologists use to construct geological histories. Note that unconformities, which on the diagram above are symbolized by the irregular lines, are indicated by dashed lines in the column below. Also, the formations that appear on the simplified stratrigraphy diagram above are marked in the table with the number that corresponds to the diagram.

Grand Canyon Stratigraphic Sequence
Geologic Time Period	Geologic Formation	Description
Triassic	------ unconformity -------
	Moenkopi Formation	Sandstone and shale, much of it red in color, with river channel cross-beds, stream ripples, and pond desiccation cracks. Also contains layers of white gypsum where ponds, lakes or coastal lagoons underwent extensive evaporation.
	------ unconformity -------
Permian	Kaibab Limestone (15)	Gray, sandy, massive, limestone up to 320' thick. Abundant fossils include corals, squids, sponges, and shellfish.
	------ unconformity -------
	Toroweap Formation (14)	Red and Yellow sandstones at the top and bottom of the formation, and some limestone between. Common fossils include corals, sponges, sharks teeth, and many kinds of clams, etc.
	------ unconformity -------
	Coconino Sandstone (13)	A massive white to buff colored, cross-bedded sandstone about 400' thick. Almost all quartz, well sorted, fine grained, and displays huge aeolian cross-bedding. trails of quadrupeds, either reptiles or amphibians, have been found.
	------ unconformity -------
	Hermit Shale (12)	100-300' thick, predominantly shale but also includes some sandstone strata. The sandstones have a deep red color. Some shale shows mud cracks and ripple marks. Fossils of plants, mostly ferns, and quadruped footprints have been found.
	------ unconformity -------
Pennsylvanian	Supai Group: (11)   Esplanade Sandstone   Wescogama Fm.   Manakacha Fm.   Watahomig Fm.	1000' thick series (group) of alternating red cross-bedded sandstones and shales. The upper part of the group is non-marine and tracks of quadrupeds are found on bed tops. These tracks are believed to have been made by amphibians or primitive reptiles. Sediments appear in many places to be thin beds spread over wide areas in short periods of time. The lower part of the Supai includes calcareous sandstones and shales which many believe are of marine origin.
	------ unconformity -------
Mississippian	Surprise Canyon Formation	Variable deposits include sands and conglomerates. Cross bedding is common but localized. Great horizontal variation in stratigraphy.
	Redwall Limestone (10)	Thick to massively bedded, bluish-gray limestone beds up to 600' high. The most conspicuous cliff in the canyon. It appears red, but that is only on the surface. Various invertebrates, including corals, shellfish, and crinoids are present as fossils.
	------ unconformity -------
Devonian	Temple Butte Limestone	A calcareous sandstone, lavender to purplish colored, 50-100' thick. Fossils of armored fish, corals, shellfish and snails have been found.
	------ unconformity -------
Cambrian	Tonto Group: Muav Limestone (9) Bright Angel Shale (8) Tapeats Sandstone (7)	The Muav Fm. is a gray to buff limestone 300-400' thick. At its base, the limestone is interbedded with green shale and sandstone. At its top the limestone grades into brown shales and sandstone. The Bright Angel Shale is mostly thinly bedded sandstones, but conspicuous micaceous shales and dolomite beds are also present. It varies between 350 and 400' thick. The Tapeats Sandstone is massive, coarse to medium grained, 100-300' thick. It is generally chocolate brown, but is lighter colored in some areas. Cross beds are very common. Ripple marks, showing strong currents in one direction can also be found. trilobite (an extinct early crab like critter) trails and worm tracks are present.
	------ unconformity -------
Middle and Late Proterozoic	Dox Sandstone (6)	Sandstone mixed with limey shale. Ripple marks and cross bedding are present. Up to 1700' thick but variable.
	Shinumo Quartzite (5)	Thick bedded, massive, white, variable color, 1100' thick in some places. Many cross beds and ripple marks on a fine scale. May form cliffs locally.
	Hakatai Shale (4)	800' thick reddish and vermilion mudstones and shales interbedded with minor sandstone. Ripple marks, mud cracks, raindrop impressions are common. This formation is generally eroded to a smooth slope.
	Bass Limestone (3)	Mostly gray dolostones, weathered dark brown in places. Up to 200' thick. Interbedded shales and sandstones are present, often showing ripple marks. Fossil algae have been found.
	------ unconformity -------
Early Proterozoic	Zoroaster Granite (2)	Though located below the Vishnu Schist in most exposures, dikes of this intrusive igneous rock actually cut through the schist in many places, and in some places, blocks of Vishnu Schist are cut off and surrounded by the Zoroaster Granite. Granites of this sort are associated with uplift and growth of mountain ranges.
	Vishnu Schist (1)	Oldest rock in the canyon. Formed by metamorphism of rocks that were originally sedimentary. The metamorphism occurred after the rocks were buried to great depth by mountain building. This formation is now tilted up and in places approaches vertical. Total thickness unknown.

You can construct an in-depth geologic history of the Grand Canyon based only on the information in the table and the cross-section above. To do so requires applying the principles of relative geologic time and the theory of the rock cycle. Included in these concepts are the theory of how different types of rock form, how they record and represent events in earth history, and how unconformities originate.

What do the rocks and structures of the Grand Canyon tell us about the geologic history of that part of the earth?

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