RADIOMETRIC DATING

Most materials decay radioactively to some extent, but the decay rates of most are so long that, for all practical purposes, they can be considered inert. The remainder are said to be radioactive. Radioactive materials can decay in any of several ways, emitting either a particle or radiation and changing to a different element or isotope. The decay rate of radioactive materials does not depend on temperature, chemical environment, or similar factors. For dating purposes, the important parameter is the half life of the reaction — the time it takes for half the material to decay. Half lives of various isotopes vary from microseconds to billions of years. Materials useful for radiometric dating have half lives from a few thousand to a few billion years.

Some types of radiometric dating assume that the initial proportions of a radioactive substance and its decay product are known. The decay product should not be a small-molecule gas that can leak out, and must itself have a long enough half life that it will be present in significant amounts. In addition, the initial element and the decay product should not be produced or depleted in significant amounts by other reactions. The procedures used to isolate and analyze the reaction products must be straightforward and reliable.

In contrast to most systems, isochron dating using rubidium-strontium does not require knowledge of the initial proportions.

Several systems are known that satisfy these constraints including carbon-14-carbon-12, Rb-Sr, Sm-Nd, K-Ar, Ar-Ar, and U-Pb. Carbon-14 has a fairly short half life and is used for dating recent organic remains. It is useful for periods up to perhaps 60,000 years and is thus very important to historians and archeologists as a method of determining the age of human artifacts. The other isotopes have half lives of hundreds of millions of years and are used for dating igneous rock formations.

Formulae related to radioactive decay

the decay constant

 λ = ln(2) / Half-life

Where λ is the decay constant, the probability of the decay of a nucleus in the same units of time as half-life.

nuclei N remaining at time t

decay rate at time t

example application

How old is a 25 gram charcoal sample that has an activity of 250 decays per minute (dpm)?

Assume Carbon-14 decays by beta particle emission to Nitrogen-14 with a half-life of 5730 years a constant ratio of carbon-14 to carbon-12 is 1.3 x 10^-12 (see Radiocarbon_dating).

solution

1. Compute the decay constant for carbon-14 (in minutes for simplification)

 λ = ln(2) / Half-life = .693/(5730yrs * 525960 min per yr) = 2.3x10-10 mins

  Number of Carbon nuclei = 25g (6.02*1023) / 12.011 = 1.26x1024

  N0 = (1.3x10-12 ) * (1.26x1024) = 1.6x1012 initial number of C-14 nuclei
  R0 = λ * N0 = (2.3x10-10) * (1.6x1012) = 368 dpm

    250dpm = 368 dpm e-λ t

    ln(250 dpm/370 dpm) = -2.3x10-10 t

    t = 0.386/2.3x10-10 = 1.678x108mins or 3190 years