The Age of the Earth

 

       Mankind has been puzzling about origins at least since the beginning of recorded history.  The age of the earth is one of the difficult puzzles that has been solved by a method not even remotely conceived or predictable until the 20th century.  The method: radioactive decay.  Early methods, widely regarded in their time as reliable, were dating from the ages of Biblical patriarchs from Adam to Abraham (or Moses?) and the time required for cooling of the initially hot and melted earth (as illustrated by volcanic eruptions).  Ages of 6000 years to 100 million years resulted.  Other early suggestions which also gave widely differing results (for various reasons) included the gradual accumulation of salt in the oceans and the total depth of sedimentary rock deposits throughout the world.

       The method using the rate of cooling of the early hot earth was found to yield a value much too short because the discovery of radioactivity didn’t occur until  1896 and radioactive decay turned out to be a significant heat source.  The heating effect of radioactive decay of uranium (and its decay products) deep in the Earth’s crust and mantle represented a new heat source totally unanticipated by any prior knowledge.  This amount of heat is very nearly adequate to explain a hot interior of the earth persisting almost indefinitely.  The reason that we think uranium is very nearly absent from the earth’s core will be mentioned later.

        At the very beginning of the 20th century Ernest Rutherford, a native of New Zealand working in Montreal, elucidated the radioactive decay sequence of uranium through radium, radon gas to lead.   Incidentally Rutherford’s work answered a very puzzling then current question in the field of chemistry: lead had different atomic weights depending on its source, common lead (as from the lead mines of Wisconsin) or lead from radioactive ores of uranium and thorium.  Rutherford promptly suggested that analysis of these differences could yield quite an accurate value of the time elapsed since uranium ores had been deposited and that the age of the earth had to be greater than that.  The basis for Rutherford’s prompt insight about determining the age of uranium ores was that he was already aware that uranium 238 had a very long half life.  Half life refers to the time required for half the atoms originally present to decay (by radioactive transformation).  Rutherford himself demonstrated the constancy of radioactive decay by placing radon gas (a short lived decay product of uranium) in a bomb sealed in heavy steel. A temperature of 2500 degrees Celsius and pressure of 1013 atmospheres did not change the rate of decay. The different atoms of an element with different atomic weights are called isotopes.  For example: heavy water has hydrogen (deuterium) with an atomic weight of 2 instead of the atomic weight of 1 of almost all ordinary hydrogen (there are traces of deuterium in all terrestrial hydrogen). These two are the only non-radioactive isotopes of hydrogen (tritium, the fuel of hydrogen bombs is radioactive). 

        The accepted modern value for the age of the earth is 4.56 billion years within 1% accuracy (a billion is 1000 million).  The reason that it took over 50 years and the inspiration of a small army of clever people to attain this accurate number is illustrated by the problem of estimating how much common lead was present in uranium ore from the time it was deposited before it began to decay to its new lead. There is some of all the stable (non-radioactive) isotopes of lead in “common” lead.  The most interesting way of determining the primeval mix of lead isotopes in uranium ores was the analysis of iron-nickel meteorites. Some of these contain traces of lead and all iron-nickel meteorites contain (almost) no uranium.  These meteorites are fragments of the core of a rather large asteroid—large enough to have an iron core like the earth’s core.  The isotopic composition of the lead in iron meteorites when used to compute the age of those stony meteorites, which happen to contain uranium without much of their own lead, results in the 4.56 billion year figure for the age of stony meteorites. 

        Garnets are a very stable mineral.  Fragments of garnets survive erosion and even some considerable heating in the earth’s crust. Some of these residing in newer rocks turn out to be as old as meteorites.  Freshly crystallized garnets form modern sources such as volcanic lava or synthetic laboratory specimens do not acquire even traces of lead from the melt (lead is so prevalent in our environment that it could be detected in synthetic garnets prepared in any ordinary laboratory without special precautions to exclude lead), but chemical affinities of any uranium in the melt with garnet’s crystal structure frequently result in garnets with traces of uranium.  These garnets can be  especially easily dated by the above described method because garnets do not contain lead except from uranium,  and lead cannot escape from the garnet without the garnet being destroyed by melting. Dating the oldest terrestrial specimens of these tiny garnets agree with the 4.56 billion year age of stony meteorites.  This demonstrates that the earth and the asteroids were formed at the same time and strongly suggests that all the planets of our sun have a common origin occurring within a relatively brief interval of geologic time.  To a geologist brief may mean as much as nearly 100 million years.  The process of an original separation by melting of an iron core and stony crust of planets and large asteroids indicates the probable absence of uranium in the earth’s core. The iron-nickel meteorites created by the same process as the earth’s core  are available and have no uranium by actual chemical analysis.

       Uranium ores contain two radioactive isotopes of uranium   All isotopes of all elements heavier than bismuth (atomic number 87, lead is 86) are radioactive and some isotopes of common elements such as potassium are radioactive with exceedingly long half lives (rendering them harmless).    Many other naturally occurring radioactive isotopes such as thorium have been used to calculate the age of the earth confirming the 4.5 billion year figure. Uranium 238 has a half life of 4.47 billion years.  Uranium 235 (also naturally occurring in uranium ores) has a half life of 704 million years, it produces a different stable isotope of lead.  The exact isotopic composition of any sample can be determined with 1% accuracy with a modern instrument called a mass spectrometer.  These instruments are small enough and rugged enough to be sent by space-craft to other planets.  Using some very complicated arithmetic and accurate isotopic percentages of the isotopes of uranium and lead in a rock specimen, the age of the specimen can be calculated without knowing or assuming the quantities of lead isotopes present when the rock was formed.  So determining the age of the earth does not depend on analyzing meteorites after all.  The meteorites were a lot easier to explain and intrinsically more interesting than the complicated arithmetic. With your implied consent we skipped the arithmetic.

       There are 339 naturally occurring nuclides (the total of all the isotopes of all 92 chemical elements found on earth).  1065 nuclides have been created by atomic physicists.  Even though these are artificial in that they didn’t exist on earth before particle accelerators and atomic reactors, they are not artificial in that they must have been created in supernovae when the 339 were created—they are too short  lived to have lasted for the required billions of years since our solar system was formed.  Illustration of the probable truth of this statement is plutonium 244, which required a very special effort to be detected on earth (Pu 244 has a half life of 82 million years, Pu 239 of atomic bomb fame has a half life of 24,000 years).  In 1971 8 millionths of a billionth of a gram of Pu 244 was obtained from molybdenum ore, an amount so small that on average 6 years would pass before even one of the atoms of that plutonium would decay.  So detecting plutonium in the earth’s crust required a very special effort. This miniscule quantity was demonstrated by mass spectrometry!  All of the missing “artificial” nuclides mentioned above have a half life of less than 450 million years, the expected result for a 4 billion year old earth.  10 to 20 half lives is long enough for all the rest to “disappear”. Needless to say all 1065 nuclides, “artificially” created, are  radioactive.  A really accurate age of the earth cannot be obtained by considering the missing nuclides, but our 4.56 billion year age is nicely confirmed.

 

John A. Frantz, M.D.

March 3,2004