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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.

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: $$ m = \frac \frac$$ 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].

You may have heard that the Earth is 4.54 billion years old. 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.

This was calculated by taking precise measurements of things in the dirt and in meteorites and using the principles of radioactive decay to determine an age. The rest will have decayed into a different nuclide (called a nuclide).

As a bonus, the intercept (\(b\)) of the line tells us the value of \(\text_\) because we know the line was flat when the age of the rock was zero. 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.

We will skip the isochron derivation, but you can find it elsewhere[1].We plot all our measurements and then fit a line through them.The slope of the line can then be solved for \(t\), giving us the age of the rock.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! If you think about it, the equation above is a lot like the formula for a line, \(y=mx b\) with \(y=\text_\), \(m= \left(e^-1 \right)\), \(x=\text_\), and \(b=\text_\).The mathematics of radioactive decay shows us that the number of Sr87 nuclides that exist after some time t is: $$\text_= \left(e^-1 \right)\text_ \text_ $$ We can measure \(\text_\), \(\text_\), and \(\lambda\), but we can’t measure \(\text_\) (no one was around to measure it back then). 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).

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The best-fit line shown in Figure 3 has a slope of 0.602459.

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