Half-Life and Radioisotope Dating

Rate of Decay The measurement of the time required for a radioactive material to decay is called its half-life. This is the time required for half of the nuclides in a sample to decay. Half-life of 238U is 4.5 billion years Half-life of 131I is 8.07 days Half-life of 194Po is 0.7 second

Carbon-14 Dating We have some radioactive materials in our bodies. One of the isotopes is carbon-14. Carbon-14 is an isotope of the carbon in CO2. All living things take it in during respiration.

Carbon-14 Dating Scientist use carbon-14 to date very old things.

Carbon-14 Dating Decayed carbon-14 is continually being replaced in the body. Once the organism dies the carbon-14 is no longer replaced, but what is there continues to decay. By examining the amount of carbon-14 left in the material, scientist can estimate the age of the subject. Accurate to about 20,000-50,000 years.

Practice Problems 1) A fossilized tree killed by a volcano was studied. It had 6.25 percent 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?

Practice Problems You need to find out how many times ½ (0.5) must be used as a factor to produce 0.0625. The answer is 4 times because 0.5 X 0.5 X 0.5 X 0.5 = 0.0625 4 half-lives have gone by and each half-life is 5730 years. 5730 years X 4 = 22,920 years

Practice Problems 2) A rock was analyzed using potassium-40. The half-life of potassium-40 is 1.25 billion years. If the rock had only 25 percent of the potassium-40 that would be found in a similar rock formed today, calculate how long ago the rock was formed. Potassium-40 Half-life is 1.25 billion years

1.25 billion X 2 = 2.50 billion years Practice Problems 2) Convert 25% to a decimal --- 0.5 X 0.5 = 0.25 2 half-lives have gone by. 1.25 billion X 2 = 2.50 billion years 0.25

Practice Problems 3) Ash from an early fire pit was found to have 12.5 percent as much carbon-14 as would be found in a similar sample of ash today. How long ago was the ash formed? Convert 12.5% to a decimal --- 0.5 X 0.5 X 0.5 = 0.125 3 half-lives have gone by. 5730 X 3 = 17,190 years ago 0.125

1.25 billion X 3 = 3.75 billion years old Practice Problems 4) A rock sample has 12.5% of the potassium-40 that would be present in a similar rock formed today. How old is the rock sample? Convert 12.5% to a decimal --- 0.5 X 0.5 X 0.5 = 0.125 3 half-lives have gone by. 1.25 billion X 3 = 3.75 billion years old 0.125

Practice Problems 5) How old is a piece of wood in which the carbon-14 is 3.12% of that in wood formed today? Convert 3.12% to a decimal --- 0.5 X 0.5 X 0.5 X 0.5 X 0.5 = 0.03125 5 half-lives have gone by. 5730 X 5 = 28,650 years old 0.0312

n = number of half-lives Half-life equation Amount remaining = amount of original sample 2n n = number of half-lives

An isotope of cesium (cesium-137) has a half-life of 30 years. If 1 An isotope of cesium (cesium-137) has a half-life of 30 years. If 1.0 mg of cesium-137 disintegrates over a period of 90 years, how many mg of cesium-137 would remain? amount of original sample 1.0 mg Amount remaining = 23 2n 1 half life = 30 years Therefore, 90 years is equal to how many half lives? n = 3

4. Sodium-25 was to be used in an experiment, but it took 3 4. Sodium-25 was to be used in an experiment, but it took 3.0 minutes to get the sodium from the reactor to the laboratory. If 5.0 mg of sodium-25 was removed from the reactor, how many mg of sodium-25 were placed in the reaction vessel 3.0 minutes later if the half-life of sodium-25 is 60 seconds? amount of original sample Amount remaining = 5.0 mg = 2n 23 1 half life = 60 seconds Therefore, 3 minutes is equal to how many half lives? n = 3