The Boltzmann constant and the age of the Earth


Fin Stuart (Left) and Darren Mark (right) together with ARGUS (foreground). These three are the 'go to' team for Argon isotope ratio measurements.

I am currently just at the end of a research programme to determine a value of the Boltzmann constant, the constant of nature that determines how much molecular energy (measured in joules) corresponds to what we call ‘one degree’ of temperature. We are close to getting the answer and I will update you shortly. But the experiment has involved learning about things that seem a long way from the original aim, and by chance the measurements we made and our quest for the lowest undertainty of measurement have ended up by helping improving estimates for the age of the Earth!

This happy coincidence came about because we worked out a value of the Boltzmann constant by measuring the molecular speeds in argon gas. And in order to work out our answer we needed to know how much of each of the three stable isotopes of Argon (36Ar, 38Ar, and 40Ar) there were in the particular sample of gas we used. By chance this is exactly what geologists need to know in order to work out how old rocks are. And our quest for low uncertainty led us to the world’s best laboratory, the Argon Isotope Facility in the Scottish Universities Environmental Research Council.

Their work is amazing and exploits the fact that potassium is commonly present in many rocks on Earth. One isotope of potassium (40K) is radioactively unstable and decays very slowly to yield 40Ar. Half of the potassium decays every 1.250 billion years, so even in the oldest rocks on Earth – around 4 billion years old – there is plenty of 40K left. But over time, as long as the argon cannot escape from the rock, the amount of radiogenic 40Ar increases, and the amount of radioactive 40K decreases. Measurements of the relative concentrations of 40Ar and 40K allow clever folk such Darren Mark and Fin Stuart to work out the age of the rocks!

Darren and Fin calibrate the sensitivity of their mass spectrometer (affectionately known as ARGUS) using argon from atmospheric air, and they also need to correct for the amount of atmospheric argon that might have diffused into their samples. And this is where I came in! While I was harassing them, they noticed that if they analysed their results in a slightly different way, they could reduce their uncertainty of measurement (and mine!).

And the moral is… at the start of this research I didn’t have a clue about the measurement of argon isotopes. But now I know that it is primarily through argon isotope measurements that we work out the age of rocks on Earth, and this is really important for our understanding of the Earth’s history. And since fossils are dated from measurements of the rocks in which they are found, this is how we know that the dinosaurs became extinct 65 million years ago and not (say) 23 million years ago. And at the end of the project I find that I have had my eyes opened to this area of science: I find that although my knowledge has grown, my awareness of what I don’t know has grown even faster! But mostly I am happy and proud that this interaction between metrologists and geologists has helped in a minor way to improve the accuracy of the timescale of events on Earth.

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