238U has a half life of 4.468 billion years, coincidentally close to the age of the earth. This makes it particularly useful for studying early earth processes and dating very old rocks. 238U decays by alpha decay to 234Th and on through a series of alpha and beta decays ultimately to 206Pb. This chain forms one third of the basis of U-series dating which is particularly useful for dating young rock, one application of which has been employed by members of our department for studying magma evolution and volcano building (see attached). One of the most useful tools in uranium geochronology is the fact that uranium has two relatively long lived radioactive isotopes (238U t1/2≈4.4 Gyr; 235U t1/2≈700 Myr). By measuring and considering the paired decay of these two isotopes to 206Pb and 207Pb respectively it is possible to accurately determine ages of billions of years. This is the basis of much zircon geochronology as well as the first definitive paper on the age of the earth. The seminal paper by Clair Patterson was the first study to calculate the "correct" age of the earth radiometrically. The age determined of 4.55 Ga is very close to the now commonly accepted age of 4.567 Ga. For a little inspiration and history: this work, which is world famous and basically spawned Pb-Pb geochronology was Patterson's Ph.D. thesis, and the results were first presented at a small conference in Wisconsin while he was a graduate student at the University of Chicago.
In addition to geologic applications, 238U is important in some weapons such as armor piercing rounds and a few civilian applications. Depleted uranium is uranium which consists mostly of 238U, the 235U having been separated out to make enriched uranium (the enrichment or depletion referring to the relative amount of 235U compared to naturally occurring uranium). Depleted uranium has a very high density which leads to its use as a counterweight in aircrafts, as a shield to gamma radiation for x-ray cameras and armor piercing ammunition.
For further reading see:
Patterson, C.C., Tilton, G.R., Inghram, M.G., 1955. Age of the earth. Science, 121(3134): 69-75.
Singer, B.S., Smith, K.E., Jicha, B.R., Beard, B.L., Johnson, C.M., Rogers, N.W., 2011. Tracking Open-system Differentiation during Growth of Santa Maria Volcano, Guatemala. Journal of Petrology, 52(12): 2335-2363.
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