Purpose: To introduce you to the concept of determining the ages of objects by measuring how their radioactivity decreases with time. In the first part of the lab you will learn a few rules of probability that will help you to understand how radioactivity is measured. In the second part of the lab, you will actually measure the radioactive half-life of two silver isotopes.

How do we know the age of the Earth? Our understanding of the physics of the earth and other celestial bodies depends critically on assumptions about the ages of those objects. While for the stars and galaxies, ages must be estimated indirectly, we are able to obtain direct measurements of the ages of solar system objects by determining their abundances of certain radioactive substances. Radioactive dating is a sophisticated experimental technique; we will use it only in its simplest application.

The first serious attempt to date the earth was made by Lord Kelvin (in the nineteenth century). Kelvin knew that the interior of the earth is warm and reasoned that the earth must be losing heat and cooling. He attempted to estimate the time required to cool from an initial molten state. If the earth were older than about 100 million years, how could it still be warm? His conclusion that the earth was less than 100 million years old agreed with another idea, that the power of the Sun derived from its slow gravitational contraction. However, it did not agree with the times estimated by most geologists or those required by Darwin for slow biological evolution.

It was left to Ernest Rutherford to provide the definitive method for determining how much older the Earth is. Rutherford's method was, of course, radioactive dating.

Radioactivity was discovered by Henri Becquerel in 1896 quite by accident. Becquerel was actually looking to see if fluorescent materials emitted X-rays, but instead he found that uranium salts, whether fluorescent or not, fogged his photographic plates.

There are two major forces at work in the nucleus of an atom: (1) the strong nuclear force that binds protons and neutrons together and (2) the electrostatic force by which the protons repel each other. Occasionally (in nuclei with the right combination of protons and neutrons) the repulsion wins out and one or more particles are ejected from the nucleus changing the atom. When that occurs, the atom actually changes its identity to that of a different element, with different chemical properties. We call this process radioactive decay, and we say that the first substance decayed to become the second.

In order to use radioactivity as a measurement of time, we obviously have to somehow predict when such a decay will occur. The prediction of radioactive decay is based on the theory of probability-just as is done in much of modern physics as well as gambling. So to begin, we'll examine a simple case: what happens when you toss a coin.

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