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Line graphs and radiometric dating
The decay may happen by emission of particles (usually electrons (beta decay), positrons or alpha particles) or by spontaneous nuclear fission, and electron capture.
Plotting an isochron (straight-line graph) is used to solve the age equation graphically.
U leakage would cause discordant points to plot above the cocordia. Lunar rocks also lie on the Geochron, at least suggesting that the moon formed at the same time as meteorites. Pb separated from continents and thus from average crust also plots on the Geochron, and thus suggests that the Earth formed at the same time as the meteorites and moon.
But, again, exptrapolation of the discordia back to the two points where it intersects the Concordia, would give two ages - t* representing the possible metamorphic event and t and solve for t . This argument tells when the elements were formed that make up the Earth, but does not really give us the age of the Earth. Thus, our best estimate of the age of the Earth is 4.55 billion years.
If a zircon crystal originally crystallizes from a magma and remains a closed system (no loss or gain of U or Pb) from the time of crystallization to the present, then the Discordant dates will not fall on the Concordia curve.
Sometimes, however, numerous discordant dates from the same rock will plot along a line representing a chord on the Concordia diagram. is then interpreted to be the date that the system became closed, and the younger date, t*, the age of an event (such as metamorphism) that was responsible for Pb leakage.
To see how we actually use this information to date rocks, consider the following: Usually, we know the amount, N, of an isotope present today, and the amount of a daughter element produced by decay, D*.
By definition, D* = N-1) (2) Now we can calculate the age if we know the number of daughter atoms produced by decay, D* and the number of parent atoms now present, N.
We can also construct a Concordia diagram, which shows the values of Pb isotopes that would give concordant dates.
The Concordia curve can be calculated by defining the following: ).
Pb leakage is the most likely cause of discordant dates, since Pb will be occupying a site in the crystal that has suffered radiation damage as a result of U decay.
U would have been stable in the crystallographic site, but the site is now occupied by by Pb.