HALF-LIFE Chapter 7.2 – BC Science 10

Half - life The time required for half ½ the nuclei in a sample of a radioactive isotope to decay The half life for any radioactive isotope is a constant for any radioactive isotope. Each radioisotope decays at a unique rate

Time = 0 100% sample (8 pennies) are still radioactive

Time = 1 half life 50% of sample (4 pennies) are still radioactive

Time = 2 half lives 25% of sample (2 pennies) are still radioactive

Time = 3 half lives 12.5% of sample (1 penny) still radioactive

Time = 4 half lives No more pennies are radioactive. Think about a sample with millions of atoms…

7.2 Half-life It can be difficult to determine the ages of objects by sight alone. Radioactivity provides a method to determine age. Measure the relative quantities of remaining radioactive material stable products formed. See pages 302 - 304 (c) McGraw Hill Ryerson 2007

7.2 Half-life Carbon dating measures the ratio of carbon-12 and carbon-14. Stable carbon-12 and radioactive carbon-14 exist naturally in a constant ratio. When an organism dies, carbon-14 stops being created and slowly decays. Carbon dating only works for organisms less than 50 000 years old. . See pages 302 - 304 (c) McGraw Hill Ryerson 2007

Carbon Dating – carbon-14 Living things replace the carbon-12 and carbon-14 in their bodies when they are alive. However when living things die, they do not replace the carbon-14 as carbon-14 decays into nitrogen-14 Carbon-14 takes 5715 years to decay half of its nuclei into nitrogen- 14 Carbon-12 remains unchanged. Therefore something that has been alive within the past 50000 years contains enough nuclei of remaining carbon-14 to measure. The ratio of carbon-12 and carbon-14 can estimate the age of the sample

Carbon Dating

Carbon dating This picture shows a skeleton and a model for C-14 decay. The arrows represent the amount of C-14 giving off it's radiation as time passes. Notice the amount goes down by half for every half life.

Decay Curve All decay curves for any radioactive element look the same except for the length of the half life.

The Rate of Radioactive Decay Half-life measures the rate of radioactive decay. Half-life = time required for half of the radioactive sample to decay. Strontium-90 has a half-life of 29 years. If you have 10 g of strontium-90 today, there will be 5.0 g remaining in 29 years. See pages 305 - 306 (c) McGraw Hill Ryerson 2007

The Rate of Radioactive Decay Decay curves show the rate of decay for radioactive elements. The curve shows the relationship between half- life and percentage of the original substance remaining. The Rate of Radioactive Decay The decay curve for strontium-90

Common Isotope Pairs Parent isotope = the original, radioactive material Daughter isotope = the stable product of the radioactive decay The rate of decay remains constant, but some elements require one step to decay while others decay over many steps before reaching a stable daughter isotope. See page 307 (c) McGraw Hill Ryerson 2007

Common Isotope Pairs There are many radioisotopes that can be used for dating. Carbon-14 decays into nitrogen-14 in one step. Uranium-235 decays into lead-207 in 15 steps. Thorium-235 decays into lead-208 in 10 steps. See page 307 (c) McGraw Hill Ryerson 2007

The Potassium-40 Clock Radioisotopes with very long half-lives can help determine the age of very old things. The potassium-40/argon-40 clock has a half-life of 1.3 billion years. Argon-40 produced by the decay of potassium-40 becomes trapped in rock. Ratio of potassium-40 : argon-40 shows age of rock. See pages 307 - 308

The Potassium-40 Clock See pages 307 - 308

K-40 Clock

Half-Life Practice Problems

If there are 50 grams of U-238 on day zero of radioactive decay, how much will there be after 4.5 billion years (1 Half Life)? A) 0.0 grams B) 10 grams C) 25 grams D) 50 grams

Solution to problem #1

Based on the graph, 2 half-lives equals A) 4.5 billion years. B) 9 billion years. C) 12.5 billion years. D) 18 billion years.

Solution to problem #1

Use the chart to determine the half-life of Carbon-14. A) 5,000 years B) 5700 years C) 10,000 years D) 11,400 years

Practice Problems 1. How long will it take 200 grams of Plutonium 239 (half life 24,400 years) to decay to 25 grams?

Practice Problems 1. How long will it take 200 grams of Plutonium 239 (half life 24,400 years) to decay to 25 grams?

Practice Problems 2. How many grams of iodine 131 (half life 8 days) would be left after 24 days if you start with 25 grams?

Practice Problems 1. How many grams of iodine 131 (half life 8 days) would be left after 24 days if you start with 25 grams?

Summary A half-life is the length of time required for half the nuclei in a sample of a radioactive isotope to decay into its products.

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