Radiometric Dating is the nail in the coffin of any disagreement with the age of the earth.Radiometric dating is the unquestioned technique for accurately determining the age of very old rocks to within 100,000 years.
Radiometric dating is the way the age of the earth's rocks are determined and therefore, the age of the earth.To prove that the earth is less than 4.8 billion years old, you have to totally discredit radiometric dating.
The basic principle involves the half lives of radioactive elements.
Here's a table of half-lives of some of the elements used in dating rocks.
Because the half-life of any particular nuclide is constant*, the half-life can serve as a nuclear clock to determine the ages of different objects. Half-lives for nuclear decay is unaffected by external conditions such as temperature, pressure or state of chemical combination. They lose their radioactivity at their characteristic rates.
(That's why the problem of disposal of radioactive waste is so critical.)
Here's a diagram that shows how the concept works.
Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting ionizing particles and radiation. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide.
By knowing the rate of decay and looking at the ratio of parent/daughter isotopes in the rock, you can determine it age.
The principles of radiometric dating are taught in Introductory Chemistry and Introductory Physics, and Introductory Geology.
Here's a sample problem from the Introductory Chemistry book, Chapter 21. It shows how to calculate the age of a rock.
The diagrams and sample problems were taken from the following two books:
Chemistry - The Central Science, Brown, LeMay, Bursten pg. 840
Basic Physics Karl Kuhn, pg. 302
To deny that the earth is billions of years old, you have to prove that the fundamental concepts of nuclear physics and chemistry are wrong. You have to prove that all the research that has used these fundamental concepts is wrong.
Apparently, John Woodmorappe (pen name of an author who has published several articles and books with the creation science groups Answers in Genesis @ http://answersingenesis.org and the Institute for Creation Research @ http://icr.org has tried to do just that. He is the author of The Mythology of Modern Dating Methods http://www.amazon.com/Mythology-Modern-Dating-Methods-Woodmorappe/dp/0932766579/ref=sr_1_4?ie=UTF8&s=books&qid=1236143096&sr=8-4.
I can't find it anymore but, one of Woodmorappe's themes is the errors found in dating techniques. He presents a table of actual ages (don't know how he got them) and dated ages OMITTING ALL THE CORRECT OBSERVATIONS! He then chuckles at the discrepancies. But, when the the erroneous results are plotted, they form a very tight grouping about the expected value!
Woodmorappe isn't even a geologist. A REAL geologist, Dr. Kevin R. Henke @ http://www.noanswersingenesis.org.au/henke_on_woody.htm from the University of Kentucky, has written over forty articles which disembowel Woodmorappe's statements on geology, various radiometric methods and the overall capabilities of radiometric dating, and accusing him of misquoting sources to support his argument