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Statistical probablity is the only thing we can know exactly.Often students get bogged down in the fact that they don't "understand" how and why radioactive elements decay and miss the whole point of this exercise.Half-life is a very important and relatively difficult concept for students.Mathematically, the half-life can be represented by an exponential function, a concept with which entry-level students may not have much experience and therefore may have little intuition about it.Instead, it is really the Problem solving in the geosciences was forever changed with the discovery of radioactivity.Radioactive elements can be used to understand numerical age of geological materials on time scales as long as (and even longer than) the age of the Earth.
The number associated with an isotope is its atomic mass (i.e., protons plus neutrons).
Showing this plot and asking them questions about the shape and changes in number of isotopes through time may help students to develop some intuition about half-life.
Although most introductory students may not be prepared for the equation for exponential decay, discussion of half-life and radioactive decay prepares entry-level students for the introduction of more mathematical discussion of exponential growth and decay in upper level classes.
They may ask, "What's the difference between an isotope and an atom?
" Another way of explaining it is that when geologists talk about isotopes, they are talking about one element of differing masses.