# Radioactive carbon dating formula and method

## Radioactive dating

Any of several methods for determining the age of archaeological and fossil remains,rocks,etc,by measuring some property of the organic or inorganic matter that changes with time.This property may be dependent on some aspect of nuclear decay,such as the decay of the radiocarbon or the uranium series ,thermo luminescence ,or electron spin resonance.These aspects are studied by radiometric dating techniques.The property may alternatively be dependent on a chemical change with a time dependent rate constant ,such as amino acid racemization.

## How does radioactive carbon dating work?

## Carbon 14 dating

Radiocarbon dating (or carbon -14 dating) is a method for determining the age of objects up to 35000 years old containing matter that was once living,such as wood.Atmospheric carbon consists mainly of the stable isotope C-12 and a small but constant proportion of C-14 ,a radio nuclide of half life 5730 years resulting from the bombardment of atmospheric nitrogen by neutrons produced by the action of Cosmic rays.All living organisms absorb carbon from atmospheric CO2 ,but after death ,absorption ceases and the once constant ratio C-14/C-12 decreases due to the decay of C-14.

## Radioactive carbon dating formula

[latex]{ 14 }_{ C }\quad \longrightarrow { 14 }_{ N }\quad +e+\xrightarrow { v } [/latex]

The C-14 concentration in a sample ,found by using a sensitive counter of particles,gives an estimate of the time elapsed since death of the living organism.

The age of geological specimens,which can be many millions of years old,is determined from the proportion of a natural radio nuclide (with a very long half life ) and its daughter nuclide contained in a sample of rock or mineral.

**Potassium argon dating:**

Potassium,in combination with other elements,occurs widely in nature especially in rocks and soil.Natural potassium contains 0.001 18 % of the radioisotopes k-40 ,which decays ,with a half life of 1.28 Gega years,partly to the stable isotope of argon ,Ar -40.Determination of the ratio k-40/Ar-40 gives an estimation of ages up to about 1000000 years.