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Radioactivity 6 Half Life LOJ Feb 2004 Half Life The half-life of a radioactive substance: • is the time it takes for the number of parent atoms in a sample to halve; • is the time it takes for the count rate from the original substance to fall to half its initial level. During one half-life, half of the radioactive atoms initially present in a sample decay. This idea can be used to date materials. LOJ Feb 2004 Graphs • A plot of the activity of a sample against time shows exponential decay • From such a graph you should be able to find the half life of the sample LOJ Feb 2004 Equipment needed to measure radioactive decay LOJ Feb 2004 LOJ Feb 2004 LOJ Feb 2004 LOJ Feb 2004 Remember when Plotting Graphs • Deduct background rate from the experiment count you are given – call this ‘corrected count rate’ • Plot corrected count rate on the Y-axis and time on the X-axis. • Draw a best fit smooth curve through the points. Not a dot-todot straight line joining! LOJ Feb 2004 Remember when Plotting Graphs • At least two readings of half life should be found from the graph. • Indicate clearly how you have used the graph with dashed guide lines – use colour • Repeats should be done to check the answer is correct - they should be very similar. • The average value of these should be quoted as your answer LOJ Feb 2004 Dating Rocks • The older a sample of a particular radioactive material, the less radiation it emits. This idea can be used to date materials, including rocks. • During one half-life, half of the radioactive atoms initially present in a sample decay. This idea can be used to date materials. LOJ Feb 2004 Dating Rocks • Uranium isotopes, which have a very long half-life, decay via a series of relatively short-lived radioisotopes to produce stable isotopes of lead. The relative proportions of uranium and lead isotopes in a sample of igneous rock can, therefore, be used to date the rock. LOJ Feb 2004 Dating Rocks • The proportions of the radioisotope potassium-40 and its stable decay product argon can also be used to date igneous rocks from which the gaseous argon has been unable to escape. LOJ Feb 2004 Carbon Dating • Methods of finding out the age of artefacts that contain materials that were once alive. • When it dies a living organism takes in no more carbon from the atmosphere and the percentage of C-14 will decrease. The ratio of C-14 to total carbon is found and from this the age can be calculated. LOJ Feb 2004 How it works • Carbon Dating measures the remaining amount of the radioactive isotope carbon14 in organic matter. It can be used to date specimens as old as 35,000 years. • During its lifetime a biological entity (plant or animal) takes an active part in the carbon cycle and it contains the same proportion of the isotope as the atmosphere does (about one ten millionth of the carbon is carbon-14). LOJ Feb 2004 LOJ Feb 2004 Carbon Dating • The death of an organism terminates the incorporation of this isotope into the fabric of the entity. From the time of death onwards the proportion of carbon-14 decreases as it decays into nitrogen. LOJ Feb 2004 C-14 in total carbon The maths • By calculating the ratio of C-14 to total carbon in a sample of the artefact it is possible to work out its age. The half-life of carbon-14 is 5,600 years. • This data could be plotted on a graph LOJ Feb 2004 Initial Value Age (years) 1 part in 10 million 0 0.5 parts in 10 million 5,600 After two 0.25 parts in 10 halfmillion lives 11,200 After one halflife After three halflives 0.125 parts in 10 million 16,800 After four halflives 0.0625 parts in 10 million 22,400 Finding the Age of Rocks • The most common and accepted method of 'absolute geologic dating' (establishment of actual age) is based on the natural radioactivity of certain minerals found in rocks. • As the rate of radioactive decay of any particular isotope is known, the age of a specimen can be worked out from the ratio of the remaining isotope and its decay product. LOJ Feb 2004 LOJ Feb 2004 Dating of Igneous Rocks (Using Uranium Content) • Geologists use this method to date igneous rock samples. If you look carefully at the half-lives of isotopes in the Uranium series you appreciate that the Uranium has a much longer half-life than any of the others. • Uranium eventually decays to lead. LOJ Feb 2004 Dating of Igneous Rocks (Using Uranium Content) • So, by comparing the proportion of Uranium in the rock to the proportion of Lead produced by its decay you can work out how many half-lives it has been decaying. • Then by using the half-life of Uranium you can work out the time involved. LOJ Feb 2004 Percentage of Uranium Percentage of Lead Initial Value 100.00% 0.00% 01:00 0 After one half-life 50.00% 50.00% 01:01 4,500 After two halflives 25.00% 75.00% 01:03 9,000 After three halflives 12.50% 87.50% 01:07 13,500 After four halflives 6.25% 93.75% 01:15 18,000 LOJ Feb 2004 Ratio of Uranium to Lead Age (millions of years)