Decay equation & curve (see Chapter 16) dN/dt = - N N = number of radioactive parent atoms t = time

Isochron approach to dating: Numbers of parents and daughter atoms are changed only by radioactive decay over the lifetime of the material -mobility in fluids, weathering, hydrothermal alteration -diffusion during metamorphism (resetting) No isotopic fractionation Decay constant well-known No other reason for linear array, such as mixing For mobile elements, there are a variety of ingenious ways to improve the use of their isotope systems

Pb – Pb isochron

Concordia diagram

40 Ar- 39 Ar Dating – incremental heating curves 39 Ar is produced by neutron bombardment of 39 K in a nuclear reactor – production rate is known 39 K/ 40 K is known Ar is driven from mineral by step-wise heating Age is calculated from the 40 Ar- 39 Ar ratio

Cosmogenic & U-series isotopes – used for dating geologically recent events N/No = e - t N = Activity = A A/Ao = e  t For 14 C, Ao = decays per minute/gram C for year 1950

Complications: Ao changes due to changes in cosmic ray flux and Earth’s magnetic field Atmospheric dilution by “dead” C, local excess of reactor produced 14 C C chemical exchanges occur in the environment Chemical and biochemical reactions cause fractionation of C isotopes

Sediment accumulation rates: 10 Be 230 Th 210 Pb ln A/Ao = - t = -  thickness/rate) and slope = - /accumulation rate Sedimentation rate = thickness/accumulation time, t = thickness/rate

Mantle evolution diagrams and model ages