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Copyright ©The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Borrowed from Evolution of the Earth Seventh Edition Prothero • Dott Chapter 5 NUMERICAL DATING OF THE EARTH ASSUMPTIONS • Rocks contain radioactive minerals which are constantly disintegrating at a steady rate. • Under certain circumstances, these atomic “clocks” can be read to give a “time.” • The meaning of the “time” depends on what has happened to the rock since the “clock” was set. Radioactive elements • Not all elements are radioactive. Those that are and are the most useful for geologic dating are: • U-238 • K-40 • C-14 Half-life = 4.5 Billion years Half-life = 1.25 Billion years Half-life = 5.73 Thousand years • Also, Sm-147, Rb-87, Th-232, U-235 U-238 DECAY • Often elements decay according to a complex decay scheme in which a host of intermediate products, many themselves radioactive, are produced. • U-238 is such and element, and given its importance to geologic dating, it is worthwhile to examine it decay scheme. • Keep in mind that U-238 has a half-life approximately equal to the age of the earth, 4.5 Billion years. Half-life for decay from U-238 all the way to Pb-206 is 4.5 b.y. (billion years). U-238 Decay Series Decay rates for intermediate daughter products range from <1 sec (polonium) to 1,622 years (radium 226). Fig. 5.4 Schematic diagram showing decay of radioactive parent isotope (e.g. U-238) to a daughter (e.g. Pb-206). The original isotope was sealed in a mineral grain at time of crystallization. Note changing ratio of parent/daughter after 2 half-lives. Note that to get an estimate of the geologicc age, you need the ratio of the parent isotope to the daughter isotope, e.g. two measurements. Fig. 5.5 Simple arithmetic plot of a universal isotopic decay curve. After 1 halflife 50% of parent isotope remains; after 2 half-lives, 25% remains. What happens if the vertical axis is changed from linear to logarithmic? BLOCKING TEMPERATURES • The “Blocking Temperature” is an important concept; it refers to processes that result in a “resetting” of the atomic clocks in a rock. • Essentially, it is possible to heat igneous and metamorphic rocks to high enough temperatures that they no longer behave as “closed systems”. That is some of the daughter products can “leak” out of the primary mineral, giving an erroneous parent/daughter ratio and hence a wrong age. (Age for what? How could the age be interpreted in a rock in which the blocking temperature has been reached?) Blocking temperatures for some common minerals and decay series. The blocking temperature is the temperature above which a mineral or rock no longer behaves as a closed system and the parent/daughter ratios may be altered from that due to pure radioactive disintegration. This can result in resetting the isotopic clock and/or give what are called discordant dates. These types of problems have given opponents of the radiometric dating of the Earth ammunition to attack the 4.5 Billion year age geologists cite. Inconsistent rate of change Use of daughter lead isotopes for dating. The ratios of 3 radiogenic lead isotopes to non-radiogenic lead-204 all change but at different rates. These ratios can also be used to date a rock or mineral. What might be another term for radiogenic? Fission tracks in an apatite crystal. Fission tracks are produced when an atom of U-238 disintegrates emitting an alpha particle, a Helium nucleus (He-4). This massive atomic particle causes massive structural damage in the crystal that can be revealed by etching. The number of tracks in a given area is proportional to the age of the mineral. (Why not just use the U238 to Pb-206 method directly in such cases?) Dating Using a System That Is NOT Closed Metamorphic rocks go though heating and cooling cycles which allow for redistribution of daughter isotopes. 1. Mineral crystallizes 1000 mya (1000 million = 1 billion yrs ago) 2. After 500 my (million yrs) some parent isotopes have decayed. 3. 480 mya (million yrs ago) metamorphic event redistributes daughter atoms out of crystal into adjacent rock. 4. Dating of the mineral will now yield the age of the metamorphic event instead of the age of the rock. Carbon Dating 1: Formation of Carbon-14 2: Decay of Carbon-14 3: The equation is for living organisms, and the inequality is for dead organisms, in which the C-14 then decays • Carbon has unique properties that are essential for life on Earth. Familiar to us as the black substance in charred wood, as diamonds, and the graphite in “lead” pencils, carbon comes in several forms, or isotopes. One rare form has atoms that are 14 times as heavy as hydrogen atoms: carbon-14, or 14C, or radiocarbon. • Carbon-14 is made when cosmic rays knock neutrons out of atomic nuclei in the upper atmosphere. These displaced neutrons, now moving fast, hit ordinary nitrogen (14N) at lower altitudes, converting it into 14C. Unlike common carbon (12C), 14C is unstable and slowly decays, changing it back to nitrogen and releasing energy. This instability makes it radioactive. • Ordinary carbon (12C)is found in the carbon dioxide (CO2) in the air, which is taken up by plants, which in turn are eaten by animals. So a bone, or a leaf or a tree, or even a piece of wooden furniture, contains carbon. When the 14C has been formed, like ordinary carbon (12C), it combines with oxygen to give carbon dioxide (14CO2), and so it also gets cycled through the cells of plants and animals. • We can take a sample of air, count how many 12C atoms there are for every 14C atom, and calculate the 14C/12C ratio. Because 14C is so well mixed up with 12C, we expect to find that this ratio is the same if we sample a leaf from a tree, or a part of your body. In living things, although 14C atoms are constantly changing back to 14N, they are still exchanging carbon with their surroundings, so the mixture remains about the same as in the atmosphere. However, as soon as a plant or animal dies, the 14C atoms which decay are no longer replaced, so the amount of 14C in that once-living thing decreases as time goes on. In other words, the 14C/12C ratio gets smaller. So, we have a “clock” which starts ticking the moment something dies. Obviously, this works only for things which were once living. It cannot be used to date volcanic rocks, for example. The rate of decay of 14C is such that half of an amount will convert back to 14N in 5,730 years (plus or minus 40 years). This is the “half-life.” So, in two half-lives, or 11,460 years, only one-quarter of that in living organisms at present, then it has a theoretical age of 11,460 years. Anything over about 50,000 years old, should theoretically have no detectable 14C left. That is why radiocarbon dating cannot give millions of years. In fact, if a sample contains 14C, it is good evidence that it is not millions of years old unless the 14C became present by some other What is CARBON DATING of fossils? The stable isotope of carbon is C-12. There is a constant generation of C14 in the upper atmosphere by cosmic particle bombardment of N (nitrogen). Nitrogen (N-15) emits a proton and becomes C-14. This is radioactive with a half-life of about 5,730 years. Plants and animals ingest this radioactive C-14 while they are alive. When they die, the ingestion stops, and the radioactive C-14 clock begins to count down. Timed Pair Share Could there be variations in the amount of C-14 in the atmosphere at any given time, or is this a constant? Non-carbon Dating Using Radioactive Isotopes Review There are various other radiometric dating methods used today to give ages of millions or billions of years for rocks. These techniques, unlike carbon dating, mostly use the relative concentrations of parent and daughter products in radioactive decay chains. For example, potassium-40 decays to argon-40; uranium-238 decays to lead-206 via other elements like radium; uranium-235 decays to lead-207; rubidium-87 decays to strontium-87; etc. These techniques are applied to igneous rocks, and are normally seen as giving the time since solidification. The isotope concentrations can be measured very accurately, but isotope concentrations are not dates. To derive ages from such measurements, some assumptions have to be made such as: • The starting conditions are known (for example, that there was no daughter isotope present at the start, or that we know how much was there). • Decay rates have always been constant which in some cases is not true. • Systems were closed or isolated so that no parent or daughter isotopes were lost or added which in some cases is not true. Resolve the Inconsistencies! • You could be the next Nobel Prize winner!