# Decay Behavior of Parent and Daughter Atoms. Deriving the age equation The change in the number of parent atoms is proportional to the total number of.

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Decay Behavior of Parent and Daughter Atoms

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 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=N 0 at t=0 we get: N = N 0 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 ParentFinal DaughterDecay const(/yr)Half Life (yr) Uranium(U)-238Lead-2069.8485 x 10 -10 4.47 billion Uranium(U)-235Lead-2071.55125 x 10 -10 704 million Thorium(Th)-232Lead-2084.9475 x 10 -11 14 billion Potassium(K)-40Argon(Ar)-40 Calcium(Ca)-40 4.96 x 10 -10 0.581 x 10 -10 1.25 billion Rubidium(Rb)-87Strontium(Sr)-876.54 x 10 -12 106 billion Carbon(C)-14Nitrogen(N)-141.29 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

40 Ar/ 39 Ar Dating method 40 K 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 39 Ar 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 ( 235 U and 238 U) Zircons exclude the daughter (Pb) when forming and hold the parent very tightly. Zircons have high melting temperature and resistant to alteration

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

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