It seems strange to me that in Topic 2.1.7 you will need to discuss the use of radioisotopes and yet the theory of radioactivity as such is not on the syllabus. The examples listed in the teacher’s notes in the guide on page 51 include carbon dating which, of course, is perhaps the best known of all the classic examples. Carbon dating relies upon the fact that carbon dioxide in the air contains some ¹⁴C. Living things are continually replenishing their carbon content through respiration so they contain a fixed ratio of ¹⁴C to ¹²C. Once death occurs the ¹⁴C gradually breaks down and forms nitrogen by β- emission:

Because the half-life of carbon-14 is 5730 years the ratio of  ¹⁴C to ¹²C gradually decreases and from its measured value the time that has elapsed since death can be determined accurately up to a period of about 60000 years.

The age of rocks which are of course much older can be determined by other radioisotope dating. For example ⁸⁷Rb decays to ⁸⁷Sr with a half-life of 4.88 x 10¹⁰ years (49 billion years).
 

So that different minerals containing strontium will have a different ratio of ⁸⁷Sr to ⁸⁶Sr depending on their age.

During the past twenty years archaeologists have used the analysis of isotopes of strontium in teeth to look at migratory patterns of humans as the ratio of the isotopes vary according to temperature, altitude, distance from the sea and local geology. This is a nice contemporary example to illustrate topic 2.1.7.  Strontium, a Group 2 element, is absorbed by the body through soils and through the food chain where it substitutes for calcium. Depending on its source the ratio of ⁸⁷Sr to ⁸⁶Sr varies. As the strontium is absorbed by the body it becomes fixed in tooth enamel as the person grows thus providing a permanent record of the environment that the person grew up in.

This ‘geographical signature’ has recently been used to prove beyond reasonable doubt that bones found in Magdeburg Cathedral in Germany belonged to the Anglo-Saxon Princess Eadgyth. Eadgyth was the granddaughter of Alfred the Great and is known to have to have married Otto the son of Henry, King of Saxony which was part of the German empire in 929 AD. When Henry died in 936 AD Otto became king of Germany and Eadgyth ruled as his queen until she died in 946 AD. Analysis of the ⁸⁷Sr to ⁸⁶Sr ratio of the teeth found in her tomb in Magdeburg confirmed that she had indeed spent the early part of her childhood in southern England.