Radioactive Decay Alpha Radiation – Emission of a helium nucleus Alternatively we write

Radioactive Decay Beta Radiation – nuclear emission of an electron or β particle

Radioactive Decay Gamma Radiation – emission of photons by excited or metastable nuclei

Looking at the decay more carefully, We see that it undergoes a complex chain of reactions before reaching the stable isotope. This decay chain emits 8 α particles and 6 β particles. If the half lives of the intermediate daughters are orders of magnitude less than the Parent, then the rate of decay of the daughter is equal to the rate of decay of the parent.

Geochronometers Choice of radioactive dating method depends on several factors – Age of the sample T 1/2 should be same order of magnitude as rock age so that there are an adequate number of parent and daughter products to accurately determine ratio

Geochronometers Other important factors – Amount of parent and daughter elements present in the sample Potassium is an abundant element so K – Ar dating can be used on most rocks – Was the system closed? Was daughter or parent lost or gained by some other mechanism, e.g. – Radiogenic lead may be deposited with Uranium – Argon can escape until the rock is below the closure temperature

Rubidium-strontium system We cannot assume that all strontium in rocks is due to rubidium decay so we modify the above equation

Rubidium-strontium system Four naturally occurring isotopes of strontium – 84 Sr: 0.6%, 86 Sr: 10%, 87 Sr: 7%, 88 Sr: 83% 86 Sr is not a product of radioactive decay so the amount present now should be equal to the amount present when the rock formed (t 0 )

Rubidium-strontium system Normalize our equation by 86 Sr to get This is a straight line with slope (e λt -1) and the intercept gives 87 Sr/ 86 Sr at the time the rock formed. Assumes that the initial Sr ratio was the same for all the minerals in rock or for all the rocks in a single location The straight line is called an isochron

Rubidium-strontium system Disadvantages – Rubidium and strontium are mobile – Rubidium does not occur in limestone or ultramafic rocks

Rubidium-strontium system The [ 87 Sr/ 86 Sr] 0 is an indicator of the rock origin – Rocks derived directly from the mantle will have an initial ratio of less than.704 – Rocks derived from remelting of crustal rocks will have a initial ratio substantially greater than 0.704

Rubidium-strontium system Since t 1/2 is much larger than the age of the earth, we can make the approximation for any rock Then plotting 87 Sr/ 86 Sr vs t defines the growth curve

Uranium-lead system Three naturally occurring isotopes of uranium – 238 U: 99.3%, 235 U: 0.7%, 234 U: 0.006% – 238 U and 235 U are used for dating

Concordia Diagrams If a system has been closed to uranium and lead and a correction is made for initial lead then the isotope ratios will plot on the concordia – an ideal plot of 206 Pb/ 238 U vs 207 Pb/ 235 U If lead or uranium are lost or gained then the ratios will lie along a straight line that intersects the concordia at the time the rock crystallized (t) and when it was disturbed (t). This line is called the discordia.

U-Pb and Pb-Pb isochrons

U-Pb isochrons often fail because of extensive uranium loss Pb-Pb isochron is a straight line

Th-Pb The Th-Pb system can be more successful than U-Pb isochrons because thorium and lead tend to be less mobile than uranium

Argon-Argon The argon-argon method depends on bombarding a sample with fast neutrons in a nuclear reactor converting some of the 39 K into 39 Ar Modern technique utilizes a laser to heat individual mineral grains or targeted spots within grains to release the argon after being irradiated. 39 Ar is unstable with half life of 269 yr

Argon-Argon The amount of 39 Ar produce is given by

Ar-Ar Now using the equation we derived previously for 40 K decay to 40 Ar we arrive at the following relations

Ar-Ar If we irradiate a standard sample (sample of known age, t s ) at the same time then we can determine J And we can now find the age of our sample using

etricdating.html Fission Track Dating 238 U undergoes spontaneous fission releasing two or three neutrons and a large amount of energy – λ s =8.46x yr -1 – λ =1.55x yr -1 Passage of charged particle results in a damage zone along its path or fission track Energy below a certain threshold leaves no track so the types of reactions recorded are limited

Fission Track Dating 238 U can then be considered as undergoing a dual decay mechanism similar to the K-Ar-Ca system

Fission Track Dating Induced fission of 235 U can be used to simplify dating problem – Requires bombarding sample with neutrons in a nuclear reactor

Fission Track Dating Then taking the ratios we have

Fission Track Dating A major advantage of fission track dating is that the stability of the tracks is temperature dependent. – Healing of damaged zones is called annealing – Rate of annealing depends on the mineral and temperature – The temperature history of rock can then be determined by measuring dates of various minerals within the rock

Spontaneous fission tracksInduced fission tracks /dating/dat_fission.html

Samarium-neodymium T 1/2 for 147 Sm- 143 Nd is 106 Gy so this system is good for dating very old rocks – Meteorites and some basalts Abundance < 10 ppm 147 Sm/ 144 Nd are ~ in present rock samples Advantage of this system is that geochemical processes do not preferentially separate Sm-Nd

Samarium-neodymium [ 143 Nd/ 144 Nd] 0 gives and indication of the rocks origin similar to the Rb-Sr system – Concentration of 143 Nd has increased through time because of 147 Sm decay – Model time dependence of 143 Nd/ 144 Nd by assuming the that the ratio in the earth is the same as chondritic meteorites

CHUR model CHondritic Uniform Reservoir

Age of the Earth Oldest rocks are found on the cratons – ancient continental cores – Acasta gneisses in Canada – 3962 Ma (U-Pb) – Isua supracrustal rocks in Greenland – 3772 Ma (Sm-Nd) and 3769 (U-Pb) So by 4000 Ma continents existed

Age of the Earth Meteorites are thought to have common origin with the planets – Chondrites are most common (90%) and contain chondrules (small glassy spheres of silicate) indicating heating followed by rapid cooling – Achondrites are crystalline silicates with no chondrules and low metal concentrations – Iron

Lead Evolution of the Earth Holmes-Houtermans model – Assumes that earth quickly differentiated in to mantle and core then U-Pb ratio changed only as a result of radioactive decay – Further assumes that lead minerals completely separated from U and Th when formed

Lead Evolution of the Earth Holmes-Houtermans model – Can be used with meteorites because they are closed system with t=0 Yields ages of between 4530 and 4570 Ma