Decay equation & curve (see Chapter 16)

dN/dt = -NN = 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

40Ar-39Ar Dating – incremental heating curves

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

• Cosmogenic & U-series isotopes – used for dating geologically recent events

N/No = e-t

N = Activity = AA/Ao = et

For 14C, Ao = 13.56 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 14C•C chemical exchanges occur in the environment•Chemical and biochemical reactions cause fractionation of C isotopes

Sediment accumulation rates: 10Be230Th210Pb

ln A/Ao = -t = -thickness/rate) and slope = -/accumulation rate

Sedimentation rate = thickness/accumulation time, t = thickness/rate

Mantle evolution diagrams and model ages