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The Age of the Earth
How do we know the Age of the Earth?
Radiometric dating
Adapted from The Age of the Earth , by the Branch of Isotope Geology, United
States Geological Survey, Menlo Park, California
How do we know the Age of the Earth?
The Earth is a constantly changing planet. Its crust is continually being created,
modified, and destroyed. As a result, rocks that record its earliest history have not been
found and probably no longer exist. Nevertheless, there is substantial evidence that the
Earth and the other bodies of the Solar System are 4.5-4.6 billion years old, and that the
Milky Way Galaxy and the Universe are older still. The principal evidence for the
antiquity of Earth and its cosmic surroundings is:
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The oldest rocks on Earth, found in western Greenland, have been dated by four
independent radiometric dating methods at 3.7-3.8 billion years. Rocks 3.4-3.6
billion years in age have been found in southern Africa, western Australia, and
the Great Lakes region of North America. These oldest rocks are metamorphic
rocks but they originated as lava flows and sedimentary rocks. The debris from
which the sedimentary rocks formed must have come from even older crustal
rocks. The oldest dated minerals (4.0-4.2 billion years) are tiny zircon crystals
found in sedimentary rocks in western Australia.
The oldest Moon rocks are from the lunar highlands and were formed when the
early lunar crust was partially or entirely molten. These rocks, of which only a few
were returned by the Apollo missions, have been dated by two methods at
between 4.4-4.5 billion years in age.
The majority of the 70 well-dated meteorites have ages of 4.4-4.6 billion years.
These meteorites, which are fragments of asteroids and represent some of the
most primitive material in the solar system, have been dated by 5 independent
radiometric dating methods.
The "best" age for the Earth is based on the time required for the lead isotopes in
four very old lead ores (galena) to have evolved from the composition of lead at
the time the Solar System formed, as recorded in the Canyon Diablo iron
meteorite. This "model lead age" is 4.54 billion years.
The evidence for the antiquity of the Earth and Solar System is consistent with
evidence for an even greater age for the Universe and Milky Way Galaxy. a) The
age of the Universe can be estimated from the velocity and distance of galaxies
as the Universe expands. The estimates range from 7 to 20 billion years,
depending on whether the expansion is constant or is slowing due to gravitational
attraction. b) The age of the Galaxy is estimated to be 14-18 billion years from
the rate of evolution of stars in globular clusters, which are thought to be the
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oldest stars in the Galaxy. The age of the elements in the Galaxy, based on the
production ratios of osmium isotopes in supernovae and the change in that ratio
over time due to radioactive decay, is 8.6-15.7 billion years. Theoretical
considerations indicate that the Galaxy formed within a billion years of the
beginning of the Universe. c) Combining the data from a) and b), the "best, i.e.,
most consistent, age of the universe is estimated to be 14-17 billion years.
Radiometric dating
Spontaneous breakdown or decay of atomic nuclei, termed radioactive decay, is the
basis for all radiometric dating methods. Radioactivity was discovered in 1896 by
French physicist Henri Becquerel. By 1907 study of the decay products of uranium (lead
and intermediate radioactive elements that decay to lead) demonstrated to B. B.
Boltwood that the lead/uranium ratio in uranium minerals increased with geologic age
and might provide a geological dating tool.
As radioactive parent atoms decay to stable daughter atoms (as uranium decays to
lead) each disintegration results in one more atom of the daughter than was initially
present and one fewer atom of the parent. The probability of a parent atom decaying in
a fixed period of time is always the same for all atoms of that type regardless of
temperature, pressure, or chemical conditions. This probability of decay is the decay
constant. The time required for one-half of any original number of parent atoms to decay
is the half-life, which is related to the decay constant by a simple mathematical formula.
All rocks and minerals contain long-lived radioactive elements that were incorporated
into Earth when the Solar System formed. These radioactive elements constitute
independent clocks that allow geologists to determine the age of the rocks in which they
occur. The radioactive parent elements used to date rocks and minerals are:
Parent
Daughter
Half-life
Uranium-235
Lead-207
0.704 billion years
Uranium-238
Lead-206
4.47
Potassium-40
Argon-40
1.25
Rubidium-87
Strontium-87
48.8
Samarium-147 Neodymium-143 106
Thorium-232
Lead-208
14.0
Rhenium-187
Osmium-187
43.0
Lutetium-176
Hafnium-176
35.9
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Radiometric dating using the naturally-occurring radioactive elements is simple in
concept even though technically complex. If we know the number of radioactive parent
atoms present when a rock formed and the number present now, we can calculate the
age of the rock using the decay constant. The number of parent atoms originally present
is simply the number present now plus the number of daughter atoms formed by the
decay, both of which are quantities that can be measured. Samples for dating are
selected carefully to avoid those that are altered, contaminated, or disturbed by later
heating or chemical events.
In addition to the ages of Earth, Moon, and meteorites, radiometric dating has been
used to determine ages of fossils, including early man, timing of glaciations, ages of
mineral deposits, recurrence rates of earthquakes and volcanic eruptions, the history of
reversals of Earth's magnetic field, and the age and duration of a wide variety of other
geological events and processes.
From “Introduction to Planetary Geology” by Billy Glass
Igneous rocks (formed from Earth’s magma solidifying) containing uranium-bearing minerals can be
dated by the uranium-lead and lead-lead methods. 238U and 235U decay to the stable lead isotopes 206Pb
and 207Pb, respectively. 238U decays to 206Pb with a half-life of 4.51 billion years. 235U decays to 207Pb with
a half-life of 0.713 billion years. All naturally-occurring uranium contains 238U and 235U in the ratio
137.7/1. Since these two uranium isotopes both decay at different decay rates, they can be used to
cross-check each other when used to date geological material. In order to use these decay schemes for
dating, the original amount of 206Pb and 207Pb present in the material must be determined. Fortunately,
there is a lead isotope, 204Pb, that is not produced by radioactive decay. The abundance of this isotope
can be used to estimate the initial amount of 206Pb and 207Pb in the material.
As a result of radioactive decay through time, the amounts of 238U and 235U have decreased and 206Pb
and 207Pb have increased. Since the uranium isotopes decay at different rates, the lead isotopes have
been increasing in quantity at different rates, and thus the ratio between 206Pb and 207Pb has
systematically changed through time. Thus the ratio 207Pb/206Pb itself forms a good radiometric clock
which is useful for dating specimens over 0.5 billion years old.
How Does Radioactivity Work? Notes from Perspectives of Modern Physics by Beiser
A nucleus undergoing radioactive decay spontaneously emits a helium nucleus (“alpha particle”), an
electron (“beta particle”), or a photon (gamma ray). Regardless of when the period of observing starts,
the activity drops to half of what it is at the start of the period in a duration equal to the “half life”. This
is because there is a certain probability that the nucleus will undergo decay in any interval of time. This
probability remains constant over time.
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Number of
Fraction Percentage
half-lives
remaining remaining
elapsed
0
1
100
1
1
50
2
1
25
3
1
12 .5
4
1
6 .25
5
1
3 .125
6
1
1 .563
7
1
0 .781
/1
/2
/4
/8
/16
/32
/64
/128
The major long-lived radioactive series progress through a series of decays until they reach a stable end
product. For example, 92U238 [the “atomic number”, equal to the number of protons, is 92, and the
atomic weight (roughly the sum of protons and neutrons) is 238] decays to the stable end product
206
, lead. The half life is 4.5 billion years. It does this through a series of alpha decays (loses two
82Pb
protons and two neutrons) and beta decays (neutron changes into proton when the electron leaves).
How does alpha decay work? Big nuclei, with 210 or more protons+neutrons, are so large that the shortrange nuclear forces that hold them together are barely able to counterbalance the mutual repulsion of
their protons. Alpha decay increases their stability by reducing their size. Why is a helium nucleus
emitted rather than, say, a proton? It turns out that other decay modes would require energy to be
supplied from the outside, whereas only the alpha particle can be emitted spontaneously with positive
energy.
There remains the problem of how the helium nucleus escapes from the heavy nucleus. An energy of 25
Mev (25 million electron volts) is necessary to escape the strong nuclear force holding the nucleus
together, but the alpha particles only have energies that range from 4 to 9 Mev. How do they get out?
With classical physics, they can’t. But quantum mechanics provides a straightforward explanation. That
this theory works so well was an early confirmation of quantum mechanics.
We start by regarding the alpha particle as a wave. (So this is one of the mysteries of quantum
mechanics, that we must regard particles as also waves in order to explain what happens in the world.
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This approach works extremely well in explaining the micro-world, explaining everything that happens,
but does not make intuitive sense. There is a lot that we really don’t understand. If the “wall” that the
particle has to get over on either side is extremely high, the particle is indeed confined to be within the
wall. It turns out that any particles that don’t have an integer number of wavelengths within the box will
interfere with themselves and break down. So only the energy levels corresponding to a certain number
of wavelengths are allowed.
Particle in a box (wikipedia)
When the wall is lower, the wave has a nonzero but small value outside the wall. In quantum mechanics,
we can’t say exactly where the particle is (Heisenberg’s “Uncertainty Principle”) but we can say with
what probability we will find it at each location. We can calculate the probability that it will actually be
outside the boundary, and this chance is nonzero. When we calculate this probability, it agrees with
what we observe. So we get alpha decay due to the probability that the particle can get outside the
boundary (the energy wall is not that high; the force holding the particle in is not that strong). Once the
helium nucleus gets far enough away, the repulsion of its two protons relative to the many protons still
in the nucleus pushes it further away.
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Particle in a finite box, showing quantum mechanical “tunneling” which can’t happen classically. Source:
http://depts.washington.edu/chemcrs/bulkdisk/chem455A_aut10/notes_Lecture%2010.pdf
(from internet searches) Beta decay was not understood until much later, and involves converting
quarks inside the nucleus from negative charge to positive charge by emitting a particle that later decays
into an electron and a neutrino. It turns out that there is a band of stability of the neutron-to-proton
ratio. If there are too many neutrons, then beta decay occurs. At low atomic numbers, a 1:1 ratio is
stable. 12C is 1:1 whereas 14C is 1.33:1 (8 neutrons and 6 protons). With more protons, more neutrons
are also necessary in order to have sufficient strong force to keep the nucleus stable, since the protons
are trying to push themselves apart. Each additional particle, proton or neutron, is added in a way that
minimizes the energy of the resulting nucleus. As the number of protons increases, so does the ratio of
neutrons to protons necessary to ensure a stable nucleus.
As opposed to alpha decay that depends on the strong nuclear force and the electromagnetic forces,
beta decay depends on the weak nuclear force. Both types of decay are needed to get from uranium to
lead.
Gamma rays are emitted by excited nuclei as they decay to less excited states, just like the Sun’s light
comes from excited electrons dropping to lower energy levels and emitting a photon. The half lives of
these excited nuclei are short.
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