Radio-isotopic Method Based on disintegration of unstable nuclei –Negatron decay (n p + + - + energy) –Positron decay (p + n + + + energy) –Alpha decay ( A X A-4 Y + He)
Radioactivity-Concepts Half-life (t 1/2 ): N= N 0 /2 Mean life: =1/ Activity: # radioactive disintegrations/sec (dps) Specific activity: dps/wt. or dps/vol Units: Becquerel (Bq)=1 dps
Decay Rates: Ln (N o /N) = t t = Ln (N o /N)
To be a useful for dating, radio- isotopes must: be measurable have known rate of decay have appropriate t 1/2 have known initial concentrations be a connection between event and radioisotope
Radioactivity-based Dating Quantity of the radio-isotope relative to its initial level (e.g., 14 C). Equilibrium /non-equilibrium chain of radioactive decay (e.g., U-series). Physical changes on sample materials caused by local radioactive process (e.g., fission track).
Radiocarbon Dating 12 C: 42*10 12 ; 13 C: 47*10 10 ; 14 C: 62 tons t 1/2 = 5730 yr = 1.0209*10 -4 /yr Formed in the atmosphere: 14 N + 1 n 14 C + 1 H Decay: 14 C 14 N + -
W.F. Libbys discovery of radiocarbon S. Korffs discovery: cosmic rays generate ~2 neutrons/cm 2 sec 14 C formed through nuclear reaction. 14 C readily oxidizes with O 2 to form 14 CO 2 Libbys t 1/2 = 5568 yr.
Conventional Radiocarbon Dating Current t 1/2 = 5730±40 yr t=8033*Ln(A sample /A standard ), where A:activity. Oxalic acid is the standard (prepared in 1950). Dates reported back in time relative to 1950 (radiocarbon yr BP). A standard in 1950 = 0.227 Bq/g A standard in 2000 = 0.225 Bq/g
Conventional Radiocarbon dating Activity of 14 C needs to be normalized to the abundance of carbon: 14 C: normalized value 14 C() = 14 C –2( 13 C+25)(1+ 13 C/10 3 ) 14 C() = (1-A sample /A standard )*10 3 Radiocarbon age = 8033*ln(1+ 14 C/10 3 )
Conventional Radiocarbon dating Precision has increased Radiocarbon disintegration is a random process. If date is 5000±100: 68% chance is 4900-5100 99% chance is 4700-5300
Radiocarbon dating-Corrections Radiocarbon can be corrected by using tree-ring chronology. Radiocarbon dates can then be converted into Calendar years (cal yr).
Radiocarbon dating-Problems Two assumptions: –Constant cosmic ray intensity. –Constant size of exchangeable carbon reservoir. Deviation relative to dendrochronology due to: –Variable 14 C production rates. –Changes in the radiocarbon reservoirs and rates of carbon transfer between them. –Changes in total amount of CO 2 in atmosphere, hydrosphere, and atmosphere.
Deviation of the initial radiocarbon activity.
Bomb-radiocarbon Nuclear testing significantly increased 14 C
Bomb 14 C can be used as a tracer
Radiocarbon dating-conclusion Precise and fairly accurate (with adequate corrections). Useful for the past ~50,000 yr. Widespread presence of C-bearing substrates. Relatively small sample size (specially for AMS dates). Contamination needs to be negligible.
Other Radio-isotopes K-Ar – 40 K simultaneously decays to 40 Ca and 40 Ar(gas) –t 1/2 =1.3*10 9 yr (useful for rocks >500 kyr –Amount of 40 Ar is time-dependent –Problems: Assumes that no 40 Ar enters or leaves the system Limited to samples containing K U-series
Other radio-isotopes Uranium series – 236 U and 238 U decay to 226 Ra and 230 Th –U is included in carbonate lattice (e.g., corals) –Age determined on the abundance of decay products –Problems: Assumes a closed system Assumes known initial conditions.
Thermo-luminescence (TL) TL is light emitted from a crystal when it is heated. TL signal depends on # e - trapped in the crystal. Trapped e - originate from radioactive decay of surrounding minerals. TL signal is proportional to time and intensity. Useful between 100 yr and 10 6 yr
TL-Applications Archaeological artifacts –Heating (>500 o C) re-sets TL signal to zero –Used for dating pottery and baked sediments Sediments –Exposure to sunlight re-sets the clock –Used for dating loess, sand dunes, river sand.
TL-Problems Different response to ionization –# lattice defects –saturation Incomplete re-setting Water can absorb radiation Unknown amount of ionization
Fission-Track Dating 238 U can decay by spontaneous fission Small tracks are created on crystals (zircon, apatite, titanite) and volcanic glass. Track density is proportional to U-content and to time since the crystal formed. Useful for dating volcanic rocks (>200 kyr) Problem: tracks can heal over time