Decay Behavior of Parent and Daughter Atoms

Deriving the age equationThe 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 α N

Decay rate is different for each type of parent and is called the decay constant.

λ: Decay constant

So:

- d N / d t = λ N

Solving this equation and setting N=N0 at t=0 we get:

N = N0 exp(- λt)

The Age Equation

λ = Decay constant

D = Daughter Product

N = Parent Remaining

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:

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

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

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.

Step Heating of a Grain

Plateau Age

Inverse Isochron

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

Concordia Plot

206Pb/238U

207Pb/235U