Review of Isotopes and Radioactive Decay

One of the most important discoveries in the study of the earth is that the earth is very old compared to human civilization.  By a careful study of processes acting on the modern earth Charles Lyell was able to demonstrate that the earth must be millions of years old.  It was not until the discovery and analysis of radioactivity that it was possible to determine just how many millions of years were required.

In order to understand the use of radioactive decay as a geological clock, some basic background in isotopes and radioactive decay is required.

1.  What is the definition of an isotope?  How does this definition differ from that of an element?

2.  Complete the table below to determine the atomic number, atomic mass and isotope symbol for each of the atoms as indicated:

3.  Most isotopes are stable.   Unless disturbed by powerful outside forces, the configuration of the nucleus will remain unchanged indefinitely.  Some isotopes, however, are unstable, and will spontaneously decay into a new nuclear configuration.  Such isotopes are called radioactive isotopes.

Two of the isotopes listed in the table for question 2 are stable, while the third is unstable.  Which are the stable isotopes, and which one is unstable?

Stable: ___  ___  Unstable: ____

4.  You should be able to work any of these problems in either direction.  Try filling in the table below when you are given the isotope symbol:

5.  Unstable isotopes undergo radioactive decay.   Decay involves nuclear reactions in which fundamental changes occur to the nucleus of each atom which decays.  There are four basic types of radioactive decay, three of which are useful in the study of the earth.  You should be able to describe and distinguish alpha decay, beta decay and electron capture, and determine the daughter products from each type of decay.

An atom of ¹⁴C decays to ¹⁴N.   This is an example of ____________ decay.

An atom of ⁴⁰K undergoes electron capture.   The daughter isotope will be:

An atom of ²³⁴Pa undergoes beta decay.  The daughter isotope will be:

An atom of ²²²Rn undergoes alpha decay.   The daughter isotope will be:

6.  The half life of an isotope is the length of time it takes for half of the parent isotope to decay.  After a second half life, one half of the remaining material will decay, and so forth.  The chart at the top of this page illustrates the radioactive decay curve.  The curve is the same shape for all isotopes, only the values in years on the X axis of the graph will change.  Use the graph to answer the following questions:

A radioactive isotope decays for 150,000 years.  At the end of this time 12.5% of the isotope remains (has not decayed).  What is the half life of this isotope?

A radioactive isotope has a half life of 4 million years.   How old is a specimen in which 6.25% of the parent isotope remains?

Click here to check your answers

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