“Radioactive Clocks” or Radiometric Dating The time span of “relevant” events varies from a few centuries to billions of years ? historians ? archeologists, ? anthropologists, ? geologists, ? astrophysicists Radioactive Decay ? independent of the age of the nucleus ? unaffected by heat ? pressure, ? magnetic and electric influences in fact, all external forces. The basis for all radioactive dating methods is this constancy of decay rate. N=N0 e-λt ? Radioactive clocks are widely used for the dating of archeological and geological and cosmic materials. ? The time elapsed since the incorporation of a “long-lived” radioactive element into a closed system can be inferred from the residual activity or from the amount of elements formed in the decay. Uncertainties: ? What is the amount of the daughter present when the rocks were formed? ? Have any parent or daughter atoms been added or lost during the process? Some Naturally occurring Radioactive Isotopes and their Half-lives Radioactive Isotope (Parent) Product (Daughter) Half-life (years)  Samarium-147 Neodymium-143 106 billion  Rubidium-87 Strontium-87 48.8 billion  Rhenium-187 Osmium-187 42 billion  Lutecium-176 Halfnium-176 38 billion  Thorium-232 Lead-208 14 billion  Uranium-238 Lead-206 4.5 billion  * Potassium-40 Argon-40 1.26 billion  Uranium-235 Lead-207 0.7 billion  Beryllium-10 Boron-10 1.52 million  Chlorine-36 Argon-36 300,000  * Carbon-14 Nitrogen-14 5730  Uranium-234 Thorium230 248,000  Thorium-230 Radium-226 75,400   Radiocarbon dating The radiocarbon method was developed by a team of scientists led by the late Professor Willard F. Libby of the University of Chicago in the late 1940s. Libby later received the Nobel Prize in Chemistry in 1960: "for his method to use Carbon-14 for age determinations in archaeology, geology, geophysics, and other branches of science." According to one of the scientists who nominated Libby as a candidate for this honour; “Seldom has a single discovery in chemistry had such an impact on the thinking of so many fields of human endeavour. Seldom has a single discovery generated such wide public interest." Carbon-14  ? 14C is produced in the upper atmosphere: ? cosmic ray bombardment of molecules produces neutrons ? 14N(n,p) 14C reaction produces 14C ? 14C combines with O2 to form CO2 ? 14CO2 equilibrates with 12CO2 and is incorporated into organic matter ? Carbon dating only applicable to matter which was living 14C Equilibrium Activity Living organisms continually exchange CO2 with the atmosphere ? At equilibrium with the atmosphere ? Assumes that rate of 14C production is constant (not true)  Specific Activity of 14C ~ 15 Bq/gram total carbon 14C half-life = 5730 years Beta-minus emission to 14N Beta energy = 0.016 MeV (not very penetrating), will not come out of solid samples Samples usually oxidized to form CO2 14C in the gas is counted Required large samples (1-2 g carbon) and long counting times (up to 15 hours)   N=N0 e-λt  Figure 1: The "Curve of Knowns" after Libby and Arnold (1949). The first acid test of the new method was based upon radiocarbon dating of known age samples primarily from Egypt (the dates are shown in the diagram by the red lines, each with a ±1 standard deviation included). The Egyptian King's name is given next to the date obtained. The theoretical curve was constructed using the half-life of 5568 years. The activity ratio relates to the carbon 14 activity ratio between the ancient samples and the modern activity. Each result was within the statistical range of the true historic date of each sample. The original measurements of Libby were calibrated by using organic samples of known age—including historical artifacts from Egypt. Corrections required  Tree rings ? Bristlecone Pines ? Some living speciments > 4000 years old ? Dead specimens overlap back to ~ 8000 years old ? Same samples used for 14C dating Corrections are needed for ages greater than ~ 2000 years. E.g., 14C date of 3000 B.C. Corrected date = 3650 B.C. Suess Effect or Industrial Effect (Hans Suess, 1950) ? Burning of fossil fuel since ~ 1890 has added 12CO2 to the atmosphere ? Effectively dilutes the 14C/12C ratio by ~2% ? 1890 wood was used as a calibration standard and corrected for decay to 1950. Nuclear Weapons ? Weapons testing in the atmosphere produces enormous amounts of neutrons ? Neutrons interact with nitrogen producing 14C through the same 14N(n,p) 14C reaction. ? Maximum effect was in ~ 1963 ? The amount of 14C in the atmosphere was doubled! ? Ratio is returning to “normal” Accelerator Mass Spectrometry: A more sensitive approach 15 Bq/g beta count rate for a 1 gram sample, when there are actually ~ 1012 atoms of 14C present in the 1 gram sample is not very efficient. Accelerator Mass Spectrometry counts all atoms: the ratio of 14C to 12C can be directly measured. Sensitivity ~ 10-15 in the 14C/12C ratio has been achieved Modern techniques require only mg samples.  contaminants of mass 14: 14N 12CH2 13CH removed during the sputtering, acceleration, stripping process.. The Shroud of Turin  Said to be the burial cloth of Christ. Bears faint impression (in 3D) of a naked crucified man. ? Libby offered to carbon date the Shroud in the 1940s (sample size required was too large) AMS techniques: 1988 3 samples dated in three separate laboratories 1290-1390 A.D. dates widely publicized ? (see http://www.shroud.com) The dating controversy continues…  The shroud samples (0.25 inch x 0.25 inch ) and three control samples were put in encoded stainless steel cylinders and taken back to the three laboratories. The age of the shroud, as determined by the 14C/12C ratio measured by AMS, was found to be 1290-1390 AD (95% confidence) in a widely publicized series of 'blind' measurements at 3 AMS labs throughout the world. Potassium-40/Argon-40 Method 40K: half-life = 1.2 x 109 years Major Advantage: offers a means to eliminate daughter atoms present at time=0. ? 40K → 40Ar daughter is a noble (non-reactive) gas ? 40Ar is assumed to be completely volatilized in igneous rocks. Crystals: no gas exchange ? All 40Ar present within the crystal must have been created in situ by 40K decay. The “Age Equation” (show that this is equivalent to N=N0 e-λt )  Oldest terrestrial rocks: ~ 3.8 x 109 years Oldest meteor/moon rocks: ~ 4.5 x 109years  The Isochron Method 87Rb → 87Sr ? Three other non-radiogenic isotopes of Sr usually present along with 87Sr ? 84Sr, 86Sr, 88Sr ? The ratio of 87Sr/87Rb increases over time ? 87Sr ratios to 84Sr, 86Sr 88Sr also increase ? Plotted ratios form straight lines ? Slope proportional to the age of the sample The Age of the Earth Some of the oldest rocks on earth are found in Western Greenland. Because of their great age, they have been especially well studied. The table below gives the ages, in billions of years, from twelve different studies using five different techniques on one particular rock formation in Western Greenland, the Amitsoq gneisses. Technique Age Range (billion years) uranium-lead 3.60±0.05 lead-lead 3.56±0.10 lead-lead 3.74±0.12 lead-lead 3.62±0.13 rubidium-strontium 3.64±0.06 rubidium-strontium 3.62±0.14 rubidium-strontium 3.67±0.09 rubidium-strontium 3.66±0.10 rubidium-strontium 3.61±0.22 rubidium-strontium 3.56±0.14 lutetium-hafnium 3.55±0.22 samarium-neodymium 3.56±0.20