GEOLOGIC TIME

Horizontally bedded sedimentary strata as seen from the North Rim of the Grand Canyon illustrating the immensity of geologic time.  It took hundreds of millions of years for these strata to be deposited as layers of sediment that were eventually converted into rock.  The geologic history of the Grand Canyon region can be read from these sedimentary layers. (photo by E.L. Crisp, May 2002)

PRINCIPLES OF RELATIVE AGE DATING OF THE ROCK RECORD

INTRODUCTION

      Time is what sets geology apart from other sciences (except Astronomy).  In geology, we are talking about “deep time”;  immense spans of time that is hard for most people to comprehend.  Earth is thought to be 4.6 billion years old (based on radiometric dating of meteorites).

     The passage of geologic time is measured in two ways by geologists, relative dating and absolute dating of rocks and geologic events (here is an interesting link ( Radiometric Dating and the Geological Time Scale ) that discusses both relative dating techniques and absolute dating of rocks .   Relative ages of rocks are concerned with the relative order (chronologic order) in which geologic events have occurred in the past.  Using principles of relative age dating geologists have divided geologic time into subidivisions.  The subdivisions of geologic time are based on changes that have occurred to the surface of Earth during past times and to changes in life forms that have existed in the past (based on fossils found in rocks).  First we will discuss the principles that geolgist use to determine the relative ages of rocks.  Next, we will examine the techniques used to date rocks in an absolute manner (i.e., to determine the age of rocks in years).  NOTE: You may also wish to check out my notes for Geology 307 (Paleobiology of Dinosaurs) dealing with relative and absolute dating at the following link:  THE TIME WHEN DINOSAURS LIVED - THE MESOZOIC ERA .

     As you can see from the geologic time scale, the largest subdivisions of geologic time are Eons.  Below the level of Eons are (in decreasing order of rank) Eras, Periods, Epochs, and Ages.  The subdivisions of these episodes of time are determined by geologists based on changes that have occurred on the Earth (both in terms of physical and biologic events) in the past.
 

HISTORY OF GEOLOGY AND DISCUSSION OF GEOLOGIC TIME CONCEPTS

     There was very little advancement in geology until the middle of the eighteenth century.  This dark time (prior to mid-1700's) for all scientific and original thought was mostly due to a strict interpretation of the Book of Genesis in the Bible.  Geologic time was considered to be but a few thousand years (and some people today still adhere to a young Earth based on a literal interpretation of the Bible, here is an interesting link { Radiometric Dating: A Christian Perspective by Roger C. Wiens -- A resource paper of the American Scientific Affiliation and the Affiliation of Christian Geologists } written by a christian who is a scientist and gives support for the reality of radiometric dating of rocks and the 4.6 billion year age for Earth).  Fossils were regarded as creatures engulfed by the Biblical Flood, freaks of nature, inventions of the devil, or figured stones.

     St Auguistine of Hippo (in Algeria)(354-430 A.D.) presented one of the first time markers.  He stated that the crucifixion of Christ was a unique event from which to measure all other events.  The was the beginning of the B.C. - A. D. time scale.

     In 1650, James Ussher (1581-1665), Archbishop of Armagh, Ireland, calculated, using genealogies described in Genesis, that Earth was created on October 22, 4004 B. C.  Thus, Earth is only about 6000 years old.  (INTERESTING NOTE:  Leonardi da Vinci (1452-1519) estimated that it took 200,000 years just to deposit the sediments in the Po River Valley in Italy.)
 

Early Attempts To Date Earth

     During the 1700s and 1800s there were several attempts to determine the age of Earth based on scientific rather than religious criteria.  Frech zoologist, Georges Louis De Buffon (1707-1788) assumed Earth was orginally a molten ball and cooled to its present state.  Buffon heated iron balls of various diameters and measured the time it took them to cool.  He concluded that it took 96,000 years for Earth to cool to its present form.  Later, using mixtures of metals and nonmetals, Buffon revised his estimate to 75,000 years.  Certainly, this contrasted sharply with Ussher's 6000 year date.  However, Buffon, afraid to go against Church doctrine, stated that his theory was pure philosophical speculation.  The British physcist, Lord Kelvin (William Thomson), elaborated on this in the mid-1800s and reasoned that Earth was a maximum of 100 million years old (will be discussed later).

     Other naturalists used rates of sedimentation to estimate the age of Earth.  These estimates were based on the idea that if one could determine how long it took to deposit a certain amount of sediment, then knowing the thickness of sedimentary rock in the world, one should be able to estimate how long it took to deposit all the sedimentary rock.  The estimates by various workers varied from less than one million to greater than one billion years.  Of course, this method is fraught with difficulties.  They were really measuring the rate of rock accumulation.  Sediment is compacted prior to lithification, but different sediments compact at different rates.  Even the same sediment type will compact differently under different conditions.  But, at least these attempts showed that Earth was most likely much older than Ussher's 6000 years.

     In 1899, John Joly (an Irish geologist) attempted to estimate the age of Earth by determing how old the oceans are.  It was assumed that the oceans formed soon after Earth itself formed and that the oceans originally consisted of freshwater.  The present salinity of the oceans would be due to accumulation of dissolved salts carried into it by rivers from the land.  So if one could determine the amount of dissolved salt carried into the oceans annually, then one could estimate the age of the oceans.  Joly calculated an age of 90 million years for the age of the oceans.  However, there are problems here too.  How much salt had precipitated in the past?  How much salt had been washed back into the oceans, etc.?  Furthermore, geologist think that the oceans reached a steady-state equilibrium (in terms of salt precipitated and dissolved salt added) early in the Paleozoic Era, thus the salinity has remained fairly constant over much of geologic time.
 

Some Fundamental Geologic Principles (Steno's Principles, 1669)

     These principles are based on the work of Nicolaus Steno (1638-1686), a Danish anatomist.  Steno worked in Italy and was curious about how sediment was deposited and how rocks form.  He observed sediment transport and deposition during stream flooding near Florence, Italy.  Steno's main three principles are listed below:
.
1. Principle of Superposition:  In a sequence of sedimentary strata, the oldest layer is at the bottom
of the sequence and the strata are progressively younger toward the top of the sequence.
2. Principle of Original Horizontality:  Sedimentary strata are originally deposited in a near
horizontal manner.  Therefore, if sedimentary strata are found to be in a steeply inclined position,
some force has altered them from their orginal position.
3. Principle of Lateral Continuity:  Sedimentary strata are originally deposited over a laterally
extensive area and are continuous until they pinch out at the edge of the ancient depositional basin (or
unless removed by subsequent uplift and erosion).
 

 The Establishment Of Geology As A Science

     ABRAHAM GOTTLOB WERNER, a German professor of mineralogy at the Frieberg Mining Academy during the late 1700's,  assimilated  the  chaotic  geologic  data of his time and proposed the first widely accepted classification of rocks and a crude relative time scale.  Werner's classification was actually a modification of an earlier (1756) classification by a German mineralogist and mining engineer Johann Lehmann.  Werner's classification is summarized as follows, from youngest to oldest:

Volcanic Series:  Werner thought was minor and due to local effects of combustion of underground coal beds.

Alluvial (or Tertiary) Series:  poorly consolidated sands,  gravels, and clays which formed after the withdrawal of  the ocean from the continents.

Stratified (or Secondary) Series:  included the majority of stratified, fossiliferous rocks.

Transition Series:  thoroughly indurated limestones, dikes and sills, and thick graywackes.  Werner thought these  rocks were the first orderly deposits formed from a world wide ocean.

Primitive (or Primary) Series:  crystalline rocks, now known as igneous and high-rank metamorphic rocks.  Werner thought these were chemical precipitates from a world wide ocean before the emergence of land.
 

Neptunism Versus Plutonism

      Werner's concept, that most rocks were formed within the ocean and that igneous and metamorphic rocks were chemical precipitates from the ocean, became known as NEPTUNISM (Neptune being the god of the sea).  Werner had a very strong personality, such that his ideas were strongly impressed upon his students.  Some say that Werner retarded the science of geology, however others say, because of the heated controversies resulting from his ideas, gathering of field data was stimulated and others interested in geology became more active.

     JAMES HUTTON (1727-1797), a Scottish medical doctor, was one of the first to seriously challenge the ideas of Werner.  Hutton never practiced medicine, but was very interested in the processes which formed and shaped the earth.  Hutton was a contemporary of Werner, but displayed a much more scientific approach than Werner.  Through lab and field work he postulated that igneous rocks cooled from a molten state, not as precipitates from the ocean.

     Hutton (1788) published a paper entitled "THEORY OF THE EARTH", which laid the ground work for modern geology.  However, Hutton was a less inspiring personality than Werner, thus his ideas were overshadowed by Werner's for many years.  Hutton also wrote in a difficult style, so his ideas on the theory of the earth were not widely read or accepted until JOHN PLAYFAIR, and associate of Hutton, realized the fault and published in 1802 a book entitled "ILLUSTRATION OF THE HUTTONIAN THEORY OF THE EARTH".

     Hutton's ideas on subterranean heat causing rock material to be in a molten state until brought near to the surface became known as PLUTONISM (for Pluto, god of the underworld).  Heated controversies between the Neptunists and the Plutonists lasted about half a century, well into the mid-1800s.
 

Uniformitarianism

     One of Hutton's greatest contributions to geology and stratigraphy was his concept of UNIFORMITARIANISM.  This concept, meaning "the present is the key to the past", states that by studying geologic processes in operation today we can safely assume that such processes operated in the past and thus we can interpret rocks as a response to geologic processes.  With modification, this concept is still the basis for modern geologic thought.  We now realize that, although the processes themselves probably have not changed with time, the rates of some geologic processes may have varied drastically from time to time.  Sedimentologists today prefer the term "ACTUALISM" for the uniformitarian concept.

     Hutton also was the first to really use the "PRINCIPLE OF SUPERPOSITION", that says older rock beds (strata) are at the bottom in an undeformed sedimentary sequence of strata. However (as stated previously), Nicholas Steno (1669) has been given credit as the first to actually state that sedimentary strata are deposited layer upon layer, that younger beds are laid down on top of older beds, and that strata are initially deposited in nearly horizontal layers (PRINCIPLE OF ORIGINAL HORIZONTALITY).  Steno also suggested that sedimentary layers and lava flows are laterally extensive in all directions within a depositonal basin until they pinch out or terminate at the edges of their depositional basin  (PRINCIPLE OF LATERAL CONTINUITY).
 

William Smith and the Principle of Fossil Succession

     WILLIAM SMITH (1769-1839), an English engineer with very little formal education, was the first person to correlate rock units from one area to another.  Smith was unaware of the bitter controversy between the Neptunists and Plutonists and probably didn't care anyway.  Smith was more concerned with the practical aspects of stratigraphy.  He published the first geologic map in 1815 entitled "GEOLOGIC MAP OF ENGLAND AND WALES, WITH PART OF SCOTLAND".   Smith's map showed the aerial distribution of 31 rock units.  Smith learned to distinguish different groups of strata based on their fossil content, mineral composition, grain size, color, and position of particular strata within a sequence.  By using these criteria, particularly fossil content of the strata, he was able to correlate strata (and formations) from localities that were miles apart.  He was the first geologist to use fossils to correlate from one area to another and the first to determine that fossils of each age group of strata where characteristic for that particular age of rocks.  Thus he was the first to use the "PRINCIPLE OF FOSSIL SUCCESSION", which states that fossil organisms succeed one another in a definite and determinable order and the relative age of sedimentary strata can be determined by their fossil content.

     Because of his contributions to the science of stratigraphy, Smith became known as WILLIAM "STRATA" SMITH - FATHER OF STRATIGRAPHY.   Smith is also known as the inventor of geologic maps and the father of English geology.

     By the 1820's and 1830's enough stratigraphic and paleontologic data had accumulated to kill off Neptunism.  Cuvier and Lamarck (two French naturalists - to be discussed more fully later) had demonstrated an evolutionary succession of fossil types such that most of the rocks in Europe could be correlated by their fossil content.

     CHARLES LYELL (1797-1876) published the first textbook of geology in 1833 (actually three volumes, the first in 1830 and the last in 1833) which emphasized the Huttonian ideas of uniformitarianism.  Lyell graduated from Oxford where he studied geology, however, his main studies at Oxford were the classics and mathematics.  Upon graduation from Oxford, he went to law school in London.  Lyell practiced law for a short time, but soon his interest in geology prevailed and in 1831 he was appointed Professor of Geology at Kings College. However, he resigned the second year there.  Soon after leaving Kings College, Lyell traveled to the United States to do field geologic studies and to present lectures.  Lyell was a close friend of Charles Darwin, and no doubt the ideas of each influenced the the thought of the other.  Lyell was knighted by Queen Victoria in 1848 and upon his death in 1876 his friends petitioned for burial in Westminster Abbey, as they stated "Britain's only proper resting place for the most philosophical and influential geologist that ever lived, and one of the best men."

     In his studies of European stratigraphy, Lyell had presented a stratigraphic column with the units arranged in order of superposition and assigned to groups.  Groups were in turn, subdivisions of higher categories termed "periods".  Lyell's "periods", Primary, Secondary, and Tertiary, kept some of the characteristics  of  Werner's   classification  ( in  general  form only).  Lyell's "periods" are generally what we would refer to as ERAS today.

     Lyell's classification scheme set the pattern for the next 100 years.  Other geologists referred to Lyell's groups as systems and the systems were named according to dominant lithologic characteristics or by locality of the typical exposure.  For example, the Oolitic System (now referred to as the Jurassic System) was named for the exposures of oolitic limestone in the Jura Mountains of southern France.

     Lyell's systems were identified over broad areas and took on added meaning.  In the late 1800's and early 1900's, North American stratigraphers could correlate similar sequences of strata with intermittent unconformities to the sequences in Europe.  The eastern portion of North America also contained similar fossils to the sections described by Lyell and others in Great Britain and on the European continent.  Thus, systems began to have time significance; there had developed a clear concept of the relative ages of the major rock groups, or systems, by superposition and fossil succession.

Catastrophism

     With the work of Hutton, Smith, Lyell, and others, (1. There was a clear concept of the relative ages of the major rock groups by superposition, 2. Fossils of each system had become known, and 3. Each system appeared to have a distinct assemblage of fossils) many of the early intellectuals of the time erroneously reasoned that each system represented a chapter of earth history ending with some sort of catastrophe, killing most, if not all, forms of life.  Those who believed in this concept of catastrophic earth history became known as CATASTROPHISTS. Baron Georges Cuvier (1769-1832) is credited as the first to propose this concept to explain the rock record.  Cuvier proposed that the physical and biological history of Earth is explained by a series of sudden widespread catastrophes.  Each catastrophe killed life forms in a portion of the area affected, new life forms were created (by Divine Power) or migrated in from elsewhere.  Catastrophist views were supported by lithologic discontinuities (unconformities) at system boundaries.  These unconformities were considered recognizable and as universal relative dates on the geologic time scale (Now we know this is not always true).

     The ideas of Hutton, as adhered to by Lyell and others, implied  a  vast  amount  of  time (geologic  time  is  sometimes referred to as deep time) to account for the geologic and stratigraphic record as they observed it.  Other naturalists,  both before and after Hutton and Lyell, tried to fit the geologic and stratigraphic record into the Old Testament account of the Deluge (Great Flood) and thus they had to fit the geologic evolution of Earth into the 6000 years as given by Old Testament scholars and clergy.  Such a short time implied that geologic processes must take place at a rapid and catastrophic rate.  Thus these DILUVIANISTS (believers in catastrophic flooding and other rapid catastrophic events) were, by definition, hard core catastrophists.

BARON GEORGES CUVIER (1769-1832), a highly respected French naturalist of his time and founder of catastrophism, proposed a solution to the vexing problem of the time question which has become known as Cuvier's Compromise.  Cuvier, commonly thought of as the father of comparative anatomy and vertebrate paleontology, had been studying the fossil vertebrate remains in Tertiary deposits of the Paris Basin.  Cuvier noted a definite succession of fossil types in the Tertiary strata.  He also noted that the strata consisted of alternating marine and freshwater fauna, thus possibly implying large scale movements of land and sea.  However, Cuvier, being a highly intelligent person, reasoned that perhaps the geologic record did require more time than the orthodox clergy were allowing.  Thus Curvier came up with his compromise by suggesting that the history of the earth could be divided into three periods: 1) the DILUVIAN PERIOD (time of Noah's Flood), 2) the POST-DILUVIAN PERIOD (time after the great deluge), and 3) the ANTEDILUVIAN PERIOD (time before the great deluge).  Cuvier proposed that geology dealt with the Antediluvian Period and that the happenings during this dark, supernatural time were beyond the scope of rational scientific investigation; i.e., the scientific method could not be used to interpret the happenings or time relationships of the Antediluvian Period.

     Cuvier also believed that there were many lesser floods both before and after the great deluge and that most forms of life were killed during  these  times  of  flooding  and  subsequent uplifting of the continents.  He believed that species did not change once created, thus new species were created to repopulate the earth.  JEAN-BAPTISTE de LAMARCK (1744-1829), a pioneer French biologist, was a contemporary and fellow countryman of Cuvier and also adhered to the idea of the history of the Earth as represented by a series of floods, or inundations by a global sea.  However, Lamarck thought that geologic time was vast, as exemplified from his writings:  "Time is insignificant and never a difficulty for Nature.  It is always at her disposal and represents an unlimited power with which she accomplishes her greatest and smallest tasks."  Lamarck believed that new forms of life were created from species which survived the catastrophic mass extinctions.  He believed in heretical evolution by inheritance of acquired characteristics (sometimes referred to as Lamarckism).

      Lyell's publications eventually convinced the scientific community that Hutton's concept of uniformitarianism was the logical scientific explanation for the interpretation of earth history and geologic processes.  Thus catastrophism  (and diluvianism) and neptunism slowly died out during the last half of the nineteenth century.  Following the publication of Lyell's stratigraphic classification in 1833, later stratigraphers added to and modified his original classification until it evolved into the present relative time scale of today.  In fact, by 1900 the relative time scale was pretty much the same as it is today.
 

 Cross-Cutting Relationships and Inclusions

     In addition to the principles of relative dating already discussed (PRINCIPLE OF SUPERPOSITION, PRINCIPLE OF ORIGINAL HORIZONTALITY, PRINCIPLE OF LATERAL CONTINUITY, and PRINCIPLE OF FOSSIL SUCCESSION), two additional principles of relative dating have been used by geologists since the early days of geology.  The PRINCIPLE OF CROSS-CUTTING RELATIONSHIPS (first proposed by Hutton, but emphazized later by Charles Lyell) says that igneous intrusions and faults (fractures of the earth's crust along which displacement has occurred) are younger than the rocks that they cut across, in other words, there had to be a medium for the intrusive or faulting activity and the medium is the  older  rock  material.    Unconformities  are  also younger than the rocks that they truncate.  The PRINCIPLE OF INCLUSIONS states that inclusions of one kind of rock in another are always representative of the older rock material.  For example, if a granitic magma has intruded into a sandstone and chunks of sandstone have been incorporated into the rising magma as xenoliths, as cooling occurs there will be inclusions of sandstone in the granite and the inclusions will represent the older rock.
 

Principle Of Unconformities

     Hutton also recognized the importance of unconformities in the geologic record.  An unconformity is a surface representing a sedimentologic or temporal (time) discontinuity between the strata above and below the surface.  The surface represents missing rock material and thus is also representative of a time gap (hiatus) in the sedimentary sequence ( i.e., rocks representative of a particular episode of geologic time are missing).  The missing rock section was either eroded or was not deposited.  There are four basic type of unconformities:

1.  DISCONFORMITY:  The strata are parallel above and below unconformable surface.  The unconformable surface is an erosional surface and can usually be identified by topographic relief or pebbles (inclusions) of the older layer incorporated into the younger rocks.

 2.  PARACONFORMITY:  The strata are also parallel above and below the unconformable surface, but the surface is not an erosional surface.  The unconformable surface shows no topographic relief or inclusions, but strata of significantly different age are separated by the unconformable surface.  The difference in age (and  thus detection of the unconformable surface) of the strata above and below the surface must be accomplished using paleontologic (fossils) and/or radiometric methods.

3.  ANGULAR UNCONFORMITY:  The strata below the unconformable surface are at some angle to the strata above.  The younger strata are essentially parallel to the erosional surface, while the older strata are inclined to the erosional surface.  This type of unconformity implies tectonic deformation which folded and/or uplifted the older strata, a period of erosion then occurred which planed off the surface, followed by deposition of  sedimentary rocks roughly parallel to the erosional surface.

4.  NONCONFORMITY:  The rocks below the unconformable surface are intrusive igneous or high rank metamorphic rocks (usually referred to as basement rocks).  The unconformable surface is an erosional surface and the younger sedimentary rocks above the surface typically have inclusions of the igneous or metamorphic rocks. There may be considerable topographic relief on the surface, but the younger sedimentary layers are not intruded by the igneous rocks.

     There were several attempts during the middle to late 1800’s to determine the age of rocks and the age of the Earth in absolute terms.

1. Rates of Sedimentation – ages ranged from a few million to about 1.5 billion.
2. Salinity of the Oceans – age of 90 million years for the Earth (John Joly, 1899).
3. Lord Kelvin's (William Thomson's) Method – based on the cooling of a molten ball (the Earth).  Age of no more than 100 million years, probably about 40 million years, and life could have inhabitated Earth for only 20-25 million years.  Geologists of the mid to late 1800's thought the Earth was much older, but could not overcome the reasoning of this well known physicist.  Darwin also thought that life had existed on Earth much longer than this.  (NOTE:  This caused a real crisis in geology.  Should geologists accept Kelvin's age (it was much older than Ussher's age), even though they thought Earth was much older than the age given by Kelvin)

     There are flaws with all of the above methods!  Can you reason out what some of the flaws are?
 

Radiometric Dating of Rocks

1. Henri Becquerel discovered radioactivity in 1896 (Pitchblende, ore of Uranium, gives off some kind of energy that darkens photographic plates).
2. Marie and Pierre Currie (1903) determine that the element radium gives of heat energy.  The
fact that certain elements, like radium, are radioactive and liberate heat killed Kelvin’s basic premise.
3. Ernest Rutherford and coworkers about 1904 explained how radioactive decay works based
on new concepts in atomic theory.
4. Bertram Boltwood of Yale (1907) used Uranium-Lead radiometric methods to measure the age
of several old rocks and got ages ranging from 400 million years to 2 billion years.
5. Arthur Holmes (from about 1910 to 1927)  using Uranium-Lead and Uranium-Helium methods
produced the first calibrated (with absolute ages) geologic time scale.
6. Many thousands of samples have been radiometrically dated since the early 1900’s and the
geologic time scale has been revised many times. The absolute dates are continually being
revised as more radiometric dates are obtained.
 

Radiometric Dating of Rocks and Minerals

Review of Atomic Theory

Protons, electrons, neutrons, ions, isotopes, etc.
 

What is Radioactive Decay?

     Radioactive decay is the emission of particles and energy from the nucleus of an atom, whereby
one element is converted to another element.  The three main types of radioactive decay are alpha
decay, beta decay, and electron capture.

The three major types of radioactive decay.

     In alpha decay an alpha particle (just like a helium nucleus), consisting of two protons and two
neutrons, is ejected from the nucleus of a radioactive parent isotope, thus the atomic number
decreases by two and the atomic mass number decreases by four for the daughter isotope.  Beta
decay involves the emission of a high speed electron from the nucleus resulting in the
conversion of a neutron to a proton, thereby increasing the atomic number by one without changing
the atomic mass number for the daughter isotope.  Electron capture decay takes place when the
nucleus captures an electron from the inner electron orbits of the atom; thereby converting a proton
to a neutron; the atomic number daughter isotope decreases by one, but the atomic mass number
is unchanged.
 

How do we relate radioactive decay to geologic time?

     When speaking of a single radioactive atom, the decay process is spontaneous and
unpredictable.  However, it is statistically possible to predict how many atoms of a given element will
decay in a given amount of time.  Thus, we cannot say which atoms will decay, but knowing how
many atoms we start with, we can predict how many will decay in a certain amount of time.

     We can use an analogy of radioactive decay to a Life Insurance Company.  The Life Insurance
Company can predict (based on past statistics) how many people of a certain age group will die in a
certain time interval, but not which individuals will die.  However, the analogy breaks down when
referring to different age groups of people.  Younger age groups will have a smaller
percentage of individuals dying for a particular time period.  This is not true of radioactive decay.

     The number of atoms of a radioactive isotope (radioisotope) that decay during a given time
interval is directly proportional only to the number of atoms of the radioisotope present in the sample
(i.e., radioactive decay is proportional to the remaining concentration of radioisotope).  Thus the rate of decay, proportional to the remaining amount of radioisotope, is independent of time.  This is the basis for the concept of HALF-LIFE.  The half-life of a radioisotope is defined as “the time taken for any initial amount of atoms of a particular radioisotope to be reduced by one half (50%) through decay”.

     Two implications of the half-life concept are obvious.  If we know the ratio of parent radioisotope
to stable daughter isotope in the mineral or rock sample and if we know the half-life, then we can
determine the age of the sample.  The relationship can be expressed as follows:

Age = value of half-life for that particular radioisotope times number of half-lives elapsed.  Or, in
equation form:
 
 

 where T is the age, T1/2 is the half-life in years, and n is the number of half-lives elapsed.

     Most methods of radiometric dating are based on measurements of accumulation of stable
daughter atoms produced by a parent radioisotope.  When a mineral crystallizes, there are no
radiogenic daughter atoms of the radioisotope contained within the mineral composition, i.e., the
daughter to parent ratio is equal to zero (D/P=0).  Knowing the decay constant (k) (which can
be determined by measurement in the laboratory) of the parent radioisotope, it is possible to measure the ratio of daughter and parent isotopes (D/P) in a mineral sample (this is done with a mass spectrometer) and compute the age of the sample by the following relationship:
 
 

where k is the decay constant (expressed as number of nuclear decays per year) for a particular
radioisotope, D is the concentration of the stable daughter isotope, and P is the concentration of the
parent radioisotope.

If we assume that one half-life has elapsed, then the above equation reduces to:
 
 

Now if we want to express the general equation in terms of half-life and use log base 10 (rather than
the natural log), the general equation reduces to the following:
 
 

For example, assume we want to determine the age of a volcanic rock using the Potassium-Argon
dating method.  Potassium-40 has a half-life of 1.3 billion years.  If we determine a ratio of daughter
to parent of 3 to 1, then what is the age of the rock sample?  Substituting into the equation gives:

     T = 3.323 (1.3 x 10⁹ years) log [3 + 1] ; therefore, the age of the rock sample is 2.6 x 10⁹
     years (or 2.6 bya or Gya).

Summary of Basics of Radiometric Dating:
1. Usually only Igneous rocks can be dated radiometrically.
2. When a mineral crystallizes it has trace quantities of radioactive atoms and ideally no stable
daughter products of the particular radioisotope/stable daughter isotope pair that we are using.
3. As the parent radioisotope decays, the stable daughter isotope increases in the mineral and cannot
get out of the mineral crystal.
4. The decay rate (which is constant for a particular radioisotope) must be known.
5. The ratio of daughter to parent can then be used to calculate the age of the rock containing the
mineral.
6. There is typically a plus or minus 1% (or less) analytical error for radiometric dates.
 

Possible Sources of Error in Radiomentric Dating

     The measurement of parent radioisotopes and stable daughter isotopes in minerals and rocks
involves laboratory procedures and mass spectrometer analyses, thus there is always some error in
measurement.  However, with careful laboratory procedures, this error is minimal (in the less than 1%
range).  Some of the problems that must be considered in the determination of
radiometric dating are listed below:

1. One of  the basic premises in radiometric dating is that the minerals and rocks used as samples
have remained in a closed system since crystallization.  If parent or daughter isotopes have been
added or removed from the system, the radiometrically calculated age will not be the true age of the
mineral or rock.  Samples used for radiometric dating must be chosen that represent unaltered
igneous rock (only rarely can sedimentary rocks be dated directly).  For example, Argon leakage is a
common problem with the Potassium-Argon method.  This is because Argon (an inert gas) is easily
driven out of the crystalline structure due to weathering of the rock or any degree of metamorphism.

2. Any initial daughter product that was present at crystallization must be corrected for.  This is
routinely done in the laboratory.

3. Because, typically, only igneous minerals and rocks are being dated, inferences about the age of
sedimentary rocks are based on field geologic interpretations.  Normally, bracketed ages of
sedimentary strata are inferred using principles of cross-cutting relationships, superposition, etc.
 

Absolute Age Dating of Sedimentary Rocks

     With a few exceptions (such as the K-Ar dating of sedimentary formed glauconite or volcanic ash
deposites mixed with other sediment), radiometric dates are typically determined for igneous rocks
and minerals.  So, how do we date sedimentary rocks in an absolute way?  The relative ages of the
geologic events in a particular area must be worked out before radiometric ages can be applied.
Once the relative sequence of events in a particular field situation is determined, radiometric dates
can be obtained for igneous intrusions and/or extrusions (volcanic rocks) that bracket certain
sedimentary strata, thus giving an age range for the sedimentary strata and the included fossils.