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Let us first look at the radioactive isotopes of interest for geological dating.It is believed that the Solar System was formed from a distribution of matter known as the Solar Nebula.The next few slides explain some of the attempts made I must say that physicists and astronomers also did not help in the process of finding the correct age of the Earth.Lord Kelvin did not know about convection currents in the molten magma in the interior of the Earth nor did he know about radioactive elements which were a source of heat energy.Astronomers were discovering that the Universe is expanding and theorizing that the Universe might have started from a small compact volume less than 1.5 billion years ago.The Earth has to be younger than the Universe and this gave geologists a great deal of ammunition to aim at scientists like Arthur Holmes who believed that radio-isotope dating was a method that is capable of providing an absolute age of the earth.By the way, Patterson was responsible for banning of leaded petrol - this he achieved through a thirty year struggle with the government bodies and the petrochemical industry!A weapon as legendary as the dagger of King Tutankhamun needs an epic backstory, and last year X-ray analysis showed that the iron in the ancient blade had come from meteorites.
How these abundances are related to the elapsed time (age of the sample) is determined by radiometric equations which are described in this article.The best isotopes are those whose half lives are similar to the age of the earth - a few billion years.Meteorites are good approximation to a closed system - particularly the small spherical chondrules, that meteorites contain, are very stable and have undergone little or no change since they were formed 4.65 billion years ago.The next question is which radio-isotopes are useful for determining the age of the earth.Unstable isotopes decay with a characteristic rate - called the half-life.
In fact, we can plot the abundance of elements found in the Sun and compare this to elemental abundance of early formed meteorites and find an exact correlation in these abundances.
(There was a day when you could argue that current Unix kernels and systems were fatally flawed and you could make important improvements.
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