Measuring the speed of radioactive decay Half-life Measuring the speed of radioactive decay

Half-life = the amount of time it takes for ½ of the amount of parent isotope to decay into the daughter product. Example: 226 88 Ra  222 86 Rn + 4 2 a Half-life would equal the amount of time it takes for 10 g of Ra to decay to 5 grams of Ra Parent isotope Daughter product

Why do we care? It can be difficult to determine the ages of objects by sight alone e.g. It can be difficult to tell which rock is the oldest. Radioactivity provides a method to determine age by comparing the relative amount of remaining radioactive material to the amount of stable products formed called radio-dating

The Importance of Carbon - All life is Carbon Based - Carbon has two useful isotopes - C-14 = radioactive - C-12 = stable (makes up 98.9% of Carbon atoms)

Carbon dating measures the ratio of carbon-12 and carbon-14. When an organism dies, carbon-14 stops being produced as the organism slowly decays. Measuring the relative amounts of carbon-12 : carbon-14 is called radiocarbon dating. C-14 has a Half-life of 5730 years We can use radio dating for up to 10 half-lives of a radio active isotope So radiocarbon dating can be used to provide the age of any organism or organic material… less than 50 000 years old Using radiocarbon dating, these cave paintings of horses, from France, were determined to have been drawn 30 000 years ago.

Half-life measures the rate of radioactive decay Half-life = time required for half of a radioactive sample to decay. The half life for a radioactive element is a constant rate of decay. e.g. Strontium-90 has a half-life of 29 years. If you have 10 g of strontium-90 today, there will be 5 g remaining in 29 years. Half-lives of many common radioisotopes are listed on pg.4 of your data booklet.

When using your table of radioisotopes you must consider: 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. Carbon-14 decays into nitrogen-14 in one step Uranium-235 decays into lead-207 in fifteen steps. Thorium-235 decays into lead-208 in ten steps.

Example: Watch the decay of a 50.0 g radioactive sample of C-14 After 2nd half-life After 1st half-life 12.5 g 6.25 g After 5th half-life 3.125 g After 3rd half-life After 4th half-life 1.625 g Remember: Every time a half-life passes half of a radioactive sample decays (i.e. is reduced by a half!)

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

Back to our Example… After 2nd half-life After 1st half-life After 5th half-life After 4th half-life After 3rd half-life Half-life 1 2 3 4 5 Time (years) 5730 11460 17190 22920 28650 Amount (g) Percentage (%) 50.0 100% 25.0 50% 12.5 6.25 3.125 1.625 25% 12.5% 6.25% 3.125%

Graphing our Example: Mass vs. Half-life Mass of Sample (g) Half-lives This type of graph is called an Exponential Decay graph--- it decreases very quickly to start with and approaches zero after a long time (~10 half-lives)

Graphing our Example: % Remaining vs. Time Percentage of Sample (%) Time (years) Notice: It doesn’t matter which method you use to plot the data, the shape of the curve is the same!

So why is C-14 dating only useful for samples less than 50000 years? Mass of Sample (g) Time (years) After about 10 half-lives (for Carbon-14 approximately 50000 years) there is so little sample remaining that you cannot measure it accurately enough!

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 argon-40 : potassium-40 shows age of rock.

The Potassium-40 Clock 1. A rock is found to contain 25% potassium-40 and 75% argon-40. A) How many half-lives old is the rock? 2 half lives old B) How many years old is the rock? 2.6 billions years old 2. What is the ratio of argon-40 to potassium-40 after 5.2 billion years? 15:1 (93.75% argon-40 : 6.25% potassium-40)

PRACTICE 1 2 3 4 Complete the following tables HALF-LIFE Percent of Parent Isotope Percent of Daughter Isotope 100 1 50 2 25 75 3 12.5 87.5 4 6.25 93.75 Complete the following tables

PRACTICE 1 1/2 2 1/4 3/4 3 1/8 7/8 4 1/16 15/16 HALF-LIFE Fraction of Parent Isotope Fraction of Daughter Isotope 1 1/2 2 1/4 3/4 3 1/8 7/8 4 1/16 15/16

A rock sample contains 120 grams of radioactive isotope A rock sample contains 120 grams of radioactive isotope. The radioactive Isotope has a half-life of 5 years. HALF-LIFE Time (years) Mass (grams) 120 1 5 60 2 10 30 3 15 4 20 7.5 25 3.75

How much of the radioactive isotope is left after 25 years have passed? 3.75 How many half-lives have passed if there is only 15 g of the parent isotope left? 3 half-lives How many years have passed if there is only 7.5 g of the parent isotope left? 20 years