Geologic Dating/Time Diagrams

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Spiral Time Scale

RADIOACTIVE DECAY

MASS NUMBER = # PROTONS + # NEUTRONS
ATOMIC NUMBER = # OF PROTONS

              PARENT ISOTOPE     DAUGHTER ISOTOPE
                           234         4       230
Alpha Decay:         U -> He + Th
                             92         2         90
         Uranium-234, Alpha Particle, Thorium -230

MASS NUMBER: 234 ---> 4 + 230
ATOMIC NUMBER: 92 ---> 2 + 90

                                 235        0     235
Beta Decay:                 U -> B + Np
                                    92       -1       93
                Uranium-235, Beta Particle, Neptunium-235

                                    40         -      0       40
Electron Capture:     K + e (or B) -> Ar
                                    19               -1       18

The rate of radioactive decay of an isotope can be used in age determinations .

RADIOACTIVE DECAY

N₀ = original quantity of parent isotope

N = quantity after some elapsed time

k = the decay constant = change in quantity/change in time

In(N/N₀) = -kt =

In (quantity after some elapsed time = t)
(quantity at time = 0)

= -(rate of decay) (time, t)

t_1/2= half life = the time at which 1/2 of the parent isotope has
decayed to form daughter isotopes

Thus, time = t_1/2 when N = 1/2N₀ and the following is true:
ln[(1/2(N₀))/N₀] = -kt_1/2
In(1/2) = -kt_1/2 = -In 2

t_1/2 = 0.693/k
(t_1/2)/0.693
In(N/N₀) = -kt
t = In(N/N0)/-k

Major Radioactive Elements Used in Radioactive Dating