Radioactive Elements

1
Decay Behavior of Parent and Daughter Atoms
2
Deriving the age equation

• The change in the number of parent atoms is
  proportional to the total number of parent atoms.
• N Number of atoms
• t Time
• - d N / d t a N
• Decay rate is different for each type of parent
  and is called the decay constant.
• ? Decay constant
• So
• - d N / d t ? N
• Solving this equation and setting NN0 at t0 we
  get
• N N0 exp(- ?t)

3
The Age Equation
In geology we want to know the age of the rock
from something we can measure. Generally we
measure the amount of the parent isotope and the
amount of the daughter. So we want the previous
equation in terms of daughter and
parent. Rearranging the previous equation one can
find that
? Decay constant D Daughter Product N
Parent Remaining
4
Some Radioactive Elements Used in Geologic Dating
Parent Final Daughter Decay const(/yr) Half Life (yr)
Uranium(U)-238 Lead-206 9.8485 x 10-10 4.47 billion
Uranium(U)-235 Lead-207 1.55125 x 10-10 704 million
Thorium(Th)-232 Lead-208 4.9475 x 10-11 14 billion
Potassium(K)-40 Argon(Ar)-40 Calcium(Ca)-40 4.96 x 10-10 0.581 x 10-10 1.25 billion
Rubidium(Rb)-87 Strontium(Sr)-87 6.54 x 10-12 106 billion
Carbon(C)-14 Nitrogen(N)-14 1.29 x 10-4 5730
5
What minerals are used?

• Potassium 40 is found in
• potassium feldspar (orthoclase)
• muscovite
• amphibole
• glauconite (found in some sedimentary rocks
  rare)
• Uranium may be found in
• zircon
• urananite
• monazite
• apatite
• sphene

6
40Ar/39Ar Dating method

• 40K decays into Ca and Ar. Ca exists in most
  rocks already so better to measure Ar which is
  less likely to contaminate the sample.
• Instead of measuring the parent K in the sample,
  K is irradiated and produces 39Ar which is
  measured.
• Much more precise to measure Daughter and Parent
  at the same time.
• Very small amounts of sample can be used (grams
  to mg).
• By step heating one can sometimes determine if
  the sample has been disturbed or altered.

7
Step Heating of a Grain
8
Plateau Age
9
Inverse Isochron
10
Uranium Lead Dating

• Long half-life
• Decay constants well known
• Two isotope system (235U and 238U)
• Zircons exclude the daughter (Pb) when forming
  and hold the parent very tightly.
• Zircons have high melting temperature and
  resistant to alteration

11
Concordia Plot
206Pb/238U
207Pb/235U
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