RADIOCARBON DATING

Until the middle of the twentieth century archaeologists had a real problem. If they found a bit of pottery, an old coin, or another object while digging up a site, just how old was it? How could they tell if the object had been dropped on the ground thirty years ago or thirty centuries ago? Radio-carbon dating is a method of obtaining age estimates on organic materials which has been used to date samples as old as 50,000 years. Within archaeology it is considered an absolute dating technique. The method was developed immediately following World War II by Willard Frank Libby and coworkers and has provided age determinations in archeology, geology, geophysics, and other branches of science. He obtained a Nobel Prize for chemistry in 1960 Radiocarbon dating can be obtained on wood, charcoal, marine and freshwater shell, bone and antler, and peat and organic-bearing sediments. They can also be obtained from carbonate deposits such as tufa, calcite, marl, dissolved carbon dioxide, and carbonates in ocean, lake and groundwater sources.

How Radiocarbon Dating can Work? Dating can Work?

How can this dating work? Most living organisms absorb carbon. During its lifetime, an organism continually replenishes its supply of carbon just by breathing and eating. Carbon (C) has three naturally occurring isotopes. Both C-12 and C-13 are stable, but C-14 decays by very weak beta decay to nitrogen-14 with a half-life of approximately 5,730 years. Naturally occurring Radiocarbon is produced as a secondary effect of cosmic-ray bombardment of the upper atmosphere.

Carbon has two stable, nonradioactive isotopes: carbon-12 (¹²C), and carbon-13 (¹³C). In addition, there are tiny amounts of the unstable isotope carbon C-14 (¹⁴C) on Earth. Carbon-14 has a half-life of 5730 years and would have long ago vanished from Earth were it not for the unremitting cosmic ray impacts on nitrogen in the Earth's atmosphere, which forms more of the isotope. When cosmic rays enter the atmosphere, they undergo various transformations, including the production of neutrons. The resulting neutrons participate in the following reaction on one of the N atoms being knocked out of a Nitrogen (N₂) molecule in the atmosphere:

n + ¹⁴N → ¹⁴C + ¹H

After the organism dies and becomes a fossil, Carbon-14 continues to decay without being replaced. To measure the amount of radiocarbon left in a fossil, scientists burn a small piece to convert it into carbon dioxide gas. Radiation counters are used to detect the electrons given off by decaying C-14 as it turns into nitrogen. The amount of C-14 is compared to the amount of C-12, the stable form of carbon, to determine how much radiocarbon has decayed, therefore, dating the fossil.

Exponential Decay Formula: A = Ao * 2^(-t/k)

Radioactive decay follows the laws of Exponential decay:

$N = N_0e^{-\lambda t}. \,$

where

N 0

= number of atoms at time 0, starting point of age,

N

= number of atoms at age or time t,

${\lambda} = \frac{\ln 2}{t_{1/2}}$ = disintegration constant,

t 1 / 2

= radiocarbon half-life

It can be shown that:

$\frac{1}{\lambda}$ = radiocarbon mean or average life.

Notice that dates are customarily given in years BP which implies t(BP) = -t because the time arrow for dates runs in reverse direction from the time arrow for the corresponding ages. From these considerations and the above equation, it results:

For a raw radiocarbon date:

$t(BP) = \frac{1}{\lambda} {\ln \frac{N}{N_0}}$

and for a raw radiocarbon age:

$t = -\frac{1}{\lambda} {\ln \frac{N}{N_0}}$