Question

Explain why radioactivity can be used as a "clock" to measure the march of geologic time.

Answer 1

You can read all about "clocks in rocks" here.
http://www.sciencecourseware.com/virtualdating/files/1.0_ClocksInRocks.html

I shall be happy to critique your summary explanation.

Answer 2

While the moment in time at which a particular nucleus decays is unpredictable, a collection of atoms of a radioactive nuclide decays exponentially at a rate described by a parameter known as the half-life, usually given in units of years when discussing dating techniques. After one half-life has elapsed, one half of the atoms of the nuclide in question will have decayed into a "daughter" nuclide or decay product. The proportion of the original nuclide to its decay products changes in a predictable way as the original nuclide decays over time. This predictability allows the relative abundances of related nuclides to be used as a clock to measure the time from the incorporation of the original nuclides into a material to the present.