Activity and puzzle to illustrate how radioactive dating works:

Isotopes of certain elements are radioactive, meaning that they decay naturally to become a new element, releasing energy in the process.  The decay process takes place in the nucleus of the atom, causing a loss of a particle that changes the number of protons present.  Since number of protons in the nucleus defines which element an atom is, this process causes one atom of one element to change into one atom of another element.  The original element is called the Parent, the product element is called the Daughter.  Scientists have found that radioactive isotopes decay at rates that are characteristic of each isotope and that those rates can measured accurately in a laboratory.  This regular decay rate provides a means to measure the passage of time, like the ticking of a clock.

1) The activity below uses the decay of imaginary element X to form imaginary element Y.
2) The decay rate is such that 1/2 of the remaining X will decay to form Y every 1000 years (measured in the laboratory on a large amount of X).
3) Y is a gaseous element and evaporates whenever the rock melts, although it remains trapped in the rock when the rock is solid.
4) The rock you have contains 6 atoms of X and 42 atoms of Y (measured in the laboratory on your rock).

Question:  How old is your rock?  (Which means, in this case, how long has it been since this rock was melted?)

Method:
First figure out how much X there was to start with (which can be determined logically from the rules of radioactive decay given above).

Then cut out pieces of paper with an X on each one equal to the number of original X's in your rock and also cut out the same number of pieces of paper with Y's on them.  Use your pieces of paper to make an analog of your original rock with it's correct number of original X's and Y's.  Now, let one 1/2 life pass.  Replace the correct number of X's with Y's.  Continue this until you get your rock (6 X and 42 Y).   How many years did it take?  (answer, est2b5a.html)
 

This activity is greatly simplified from an actual measurement of a rock age.  However it illustrates the key ideas involved in an actual measurement, which are 1)  determination of the original composition of the rock  2) measurement of its present composition  3) use of known decay rate to determine how much time passed between the rocks original state and its present state.

Note:  The Potassium (K) - Argon (Ar) dating system is similar to the imaginary X-Y in that Ar also evaporates when a rock melts, although the 1/2 life for K-Ar is very much longer than 1000 years.  Other dating systems (e.g. U-Pb, Rb-Sr, Hf-Lu, Sm-Nd, C14-N) have different methods for determining where the clock is set to zero and different half-lives.  Not all parent-daughter pairs are useful for measuring the age of the Earth.  For example, the most widely known system, C14-N, has a short half life of a little over 5000 years and so is not useful for dating most geological materials which are so old that there is not enough radioactive C14 left to be measurable.

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