Nuclear Chemistry

Nuclear Chemistry Half-Life and Radioisotope Dating

Radioctive Decay/Rate of Decay • Half-life : the time it takes for half of a given amount of a radioactive isotope to undergo decay, • Symbolized by t1/2

Rate of Decay • Half life values for some commonly used radioactive isotopes

Rate of Decay • During each half life period, half of the radioactive sample decays. • What percentage of the sample is left after 1 half life? • 50% • 2 half lives? • 25% • 3 half lives? • 12.5%

Rate of Decay • Why is it important? • Radioactive decay has provided scientists a technique for determining the age of fossils, geological formations, and human artifacts. • If scientists know the half life of a particular isotope they can determine how old an object is by measuring the amount of the isotope present in the object. • 4 isotopes are commonly used for dating objects • Carbon-14 • Uranium-238 • Rubidium-87 • Potassium-40

Carbon-14 Dating • Used to determine the age of fossils • Has a half-life of 5730 years • Used to date objects up to 60,000 years old • Fossils and geologic formations older than this need to be dated with isotopes that have a longer half-life

Determining the age of a fossil • Example • You are studying a fossilized tree killed by a volcano. It had 6.25% of the amount of carbon-14 found in a sample of the same size from a tree that is alive today. When did the volcanic eruption take place? • Let’s take a step-wise approach to solving this problem….

Example-Determining the age of a fossil • You are studying a fossilized tree killed by a volcano. It had 6.25% of the amount of carbon-14 found in a sample of the same size from a tree that is alive today. When did the volcanic eruption take place? • Step 1: Analyze • What information does the problem give us? • The half-life of carbon-14 is 5730 years • The fraction of carbon-14 remaining is 6.25%, (or 0.0625 )

Example-Determining the age of a fossil • You are studying a fossilized tree killed by a volcano. It had 6.25% of the amount of carbon-14 found in a sample of the same size from a tree that is alive today. When did the volcanic eruption take place? • Step 2: Set up the problem • Calculate the number of half-lives that have passed for the carbon-14 sample • Remember, during each half-life half of the isotope decays, so we need to find out how many half-lives it takes until we have 6.25% of our carbon-14 left. • ½ x ½ x ½ x ½ = 0.0625 • 4 half-lives have gone by **Problem solving hint** -> multiply ½ by itself over and over again until you get the number, or percentage, that you want

Example-Determining the age of a fossil • You are studying a fossilized tree killed by a volcano. It had 6.25% of the amount of carbon-14 found in a sample of the same size from a tree that is alive today. When did the volcanic eruption take place? • Step 3: Solve • Because 4 half-lives have gone by and each half-life = 5730 years, multiply 5730 by 4 • 5730 x 4 = 22,920 years • Answer: The tree from which the sample was taken must have been killed by the volcano about 22,920 years ago.

Example 2- Determining the age of a fossil • Ash from an early fire pit was found to have 12.5% as much carbon-14 as would be found in a similar sample of ash today. How long ago was the ash formed? • Step 1: Analyze • The half-life of carbon-14 is 5730 years • 12.5% of carbon-14 remains

Example 2-Determining the age of a fossil • Ash from an early fire pit was found to have 12.5% as much carbon-14 as would be found in a similar sample of ash today. How long ago was the ash formed. • Step 2: Set up • ½ x ½ x ½ = 0.125 • 3 half-lives have gone by • Step 3: Solve • 3 x 5730 = 17,190 years • Answer: The ash was formed 17,190 years ago

Nuclear Chemistry