The best estimate of the earth's age comes from the Canyon Diablo iron meteorite. Using the rate of radioactive decay of uranium, scientists calculated that the earth is 4.56 billion years old.
Fundamentals of radiogenic isotope geology
Radioactive nuclides decay with a half-life. If the half-life of a material is 100 years and you have 1 kg of it, 100 years from now you will only have 0.5 kg of it. The rest will have decayed into a different nuclide (called a daughter nuclide). Several radioactive nuclides exist in nature with half-lives long enough to be useful for geologic dating.
Let’s go through an example of calculating the age of a rock with the radioactive nuclide Rubidium-87 (Rb87). This nuclide decays to Strontium-87 (Sr87) with a half-life of 48.8 billion years. Imagine going way back in time and looking at some lava that is cooling to become a rock. It naturally has different concentrations of Rb and Sr in different parts of the rock because these don’t necessarily mix perfectly. This is shown schematically in Figure 1. Once it cools all the way and crystallizes, it is considered “born” and atoms can no longer come in or out of the system. At this point, its radiometric clock starts ticking.
Figure 1. Schematic diagram of a rock with different concentrations of Rb and Sb throughout.
Though the Rb and Sr concentrations differ, it’s safe to assume that the isotopic makeup of Sr and of Rb is the same everywhere. This is the key to figuring out how much time has passed since the rock solidified. As time goes on, the Rb87 in the rock slowly turns into Sr87. Parts of the rock that have more Rb87 will end up with more Sr87. By measuring a few samples of the rock and comparing the relative amounts of Sr87 and Rb87, we can figure out how old the rock is!
The
mathematics of radioactive decay shows us that the number of Sr87 nuclides that exist after some time t is:Sr87now=(eλt−1)Rb87now+Sr87origSr87now=(eλt−1)Rb87now+Sr87orig
We can measure Sr87nowSr87now, Rb87nowRb87now, and λλ, but we can’t measure Sr87origSr87orig (no one was around to measure it back then). So what do we do? We use something called an isochron. If you think about it, the equation above is a lot like the formula for a line, y=mx+by=mx+b with y=Sr87nowy=Sr87now, m=(eλt−1)m=(eλt−1), x=Rb87nowx=Rb87now, and b=Sr87origb=Sr87orig. Because the rock originally had different mixtures of Rb and Sr, we can expect to get different points for each sample we measure, and if all samples have the same age, then we expect to see a straight line (hence the name isochron).
We plot all our measurements and then fit a line through them. The slope of the line can then be solved for tt, giving us the age of the rock. As a bonus, the intercept (bb) of the line tells us the value of Sr87origSr87orig because we know the line was flat when the age of the rock was zero. The animation in Figure 2 shows the flat line and how it increases with time.
Figure 2. The isochrons of the Rb/Sr clock. Note that the values of the axes are actually normalized by Sr86 because the mass spectrometers used to take these measurements are much more accurate at relative values than they are at absolutes. It works because Sr86 is stable and not radiogenic and therefore stays constant with time.
The isochron method can determine the age of any rock, but new rocks are formed all the time. So to figure out the age of the Earth, we have to look somewhere else… in the sky!
The age of the Earth
Earth has a molten magma layer and plate tectonics, so the “closed system” requirement of these radiometric dating methods is sometimes difficult to satisfy for Earth itself. Meteorites, on the other hand, have been floating around in space since the solar system was formed. When they come crashing to Earth, analysis of their composition can be geologically analyzed.
Claire Patterson was the first to accurately date the crystallization of Earth to 4.55 +/- 0.05 billion years ago. He used a lead isotope isochron method using measurements from three different meteorites (lead-206, lead-207 are the eventual decay products of uranium-238 and uranium-235). He then took measurements from the deep ocean that fell squarely on the meteorite isochron, suggesting that the Earth and the meteorites were both created at the same time, 4.55 billion years ago.
Many other methods have been used to date the Earth, with many different sets of radioactive nuclides (and other methods). They are all consistent with Patterson’s measurement. This is how we know how old the Earth is.
The mathematical details of the lead-lead isotopic clock are less straightforward than those of the Rb-Sr method. On the other hand, since only lead is involved (instead of two chemical species), the lead-lead clock is resilient against situations where the samples were recently weathered or otherwise “opened”. We will skip the isochron derivation, but you can find it elsewhere[1]. The end result is that the slope of the isochron with Pb207 concentrations graphed against Pb206 (both relative to non-radiogenic Pb204) is equal to:
m=NU235NU238eλU235t−1eλU238t−1m=NU235NU238eλU235t−1eλU238t−1
Data from several meteorites and from a few terrestrial sources are shown in Figure 3. The data have been replotted from the tables of [2].
Figure 3.The Pb-Pb isochron of several meteorites and deep Earth samples. Since this determines the age of the Earth, it is also known as the Geochron.
The best-fit line shown in Figure 3 has a slope of 0.602459. Unfortunately, the geochron equation above is transcendental, meaning there’s no algebraic solution for it and it has to be solved numerically.
Note that Uranium-235 decays to Lead-207 and that Uranium-238 decays to Lead-206. There are short-lived details in these decay chains, but they don’t matter on the timescales we’re dealing with.
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What are a few simple, compelling examples of proof that the Earth is much older than 6,000 years?
i provided reliable peer reviewed scientific information. You deferred to a fake story about magic written by goat herders.
