Radiometric dating (or radioactive dating) is any technique used to date organic and also inorganic materials from a process involving radioactive decay. The method compares the abundance of a naturally occurring radioactive isotope within the material to the abundance of its decay products, which form at a known constant rate of decay.

The radioactive decay law states that the probability per unit time that a nucleus will decay is a constant, independent of time. This constant is called the decay constant and is denoted by λ, “lambda”. This constant probability may vary greatly between different types of nuclei, leading to the many different observed decay rates. The radioactive decay of certain number of atoms (mass) is exponential in time.

Radioactive decay law: N = N0.e-λt

One of the oldest radiometric dating methods is uranium-lead dating. The age of the earth’s crust can be estimated from the ratio between the amounts of uranium-238 and lead-206 found in geological specimens. The long half-life of the isotope uranium-238 (4.51×109 years) makes it well-suited for use in estimating the age of the earliest igneous rocks and for other types of radiometric dating, including uranium–thorium dating and uranium–uranium dating.

Uranium-lead dating is based on the measurement of the first and the last member of the uranium series, which is one of three classical radioactive series beginning with naturally occurring uranium-238. This radioactive decay chain consists of unstable heavy atomic nuclei that decay through a sequence of alpha and beta decays until a stable nucleus is achieved. In case of uranium series, the stable nucleus is lead-206. The assumption made is that all the lead-206 nuclei found in the specimen today were originally uranium-238 nuclei.  That means at the crust’s formation the specimen contained no lead-206 nuclei. If no other lead isotopes are found in the specimen, this is a reasonable assumption. Under this condition, the age of the sample can be calculated by assuming exponential decay of uranium-238. That is:

Uranium-lead dating method is usually performed on the mineral zircon. Zircons from Jack Hills in Western Australia, have yielded U-Pb ages up to 4.404 billion years, interpreted to be the age of crystallization, making them the oldest minerals so far dated on Earth.

## Age of the Earth – Uranium-lead Dating

The age of the Earth is about 4.54 billion years. This dating is based on evidence from radiometric age-dating of meteorite material and is consistent with the radiometric ages of the oldest-known terrestrial and lunar samples.

References:

1. Knoll, Glenn F., Radiation Detection and Measurement 4th Edition, Wiley, 8/2010. ISBN-13: 978-0470131480.
2. Stabin, Michael G., Radiation Protection and Dosimetry: An Introduction to Health Physics, Springer, 10/2010. ISBN-13: 978-1441923912.
3. Martin, James E., Physics for Radiation Protection 3rd Edition, Wiley-VCH, 4/2013. ISBN-13: 978-3527411764.
4. U.S.NRC, NUCLEAR REACTOR CONCEPTS
5. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Nuclear and Reactor Physics:

1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.
9. Paul Reuss, Neutron Physics. EDP Sciences, 2008. ISBN: 978-2759800414.