It’s better to have a half-life than no life! Radioactive Decay

Radioactivity An unstable atomic nucleus emits a form of radiation (alpha, beta, or gamma) to become stable. In other words, the nucleus decays into a different atom.

What does it mean to be radioactive? Atoms that are radioactive have nuclei that spontaneously decompose to form a different nuclei and produce one or more particles These particles can be any of the following Alpha particle (42He) Beta particle (0-1e) Gamma particle (00γ)

Radioactive (cont’d) Atoms that are radioactive have a neutron/proton ratio much greater than 1 Radioactivity can be detected by a Geiger counter

What use is radioactivity? Medicine – radioactive materials are used as tracers in the body Energy sources – energy can be obtained through two nuclear processes Fission: a nucleus divides into smaller fragments Fusion: nuclei combine to form a larger nucleus

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

HALF-LIFE

Calculations for half-life As an example, Technetium-99 has a half-life of 6 hours.This means that, if there is 100 grams of Technetium is present initially, after six hours, only 50 grams of it would be left.After another 6 hours, 25 grams, one quarter of the initial amount will be left. And that goes on like this. 25

Try it!!! Now lets try to solve a half-life calculation problem… Sodium-24 has a half-life of 15 hours. How much sodium-24 will remain in an 18.0 g sample after 60 hours?

Solution Initially, Sodium -24 is 18 grams, and after 15 hours, I will have ½ of it left. 60 hours is four half lives The arrows represent the half-life. 18 g 9g 4.5g 2.25 It goes like this till it reaches ____ grams, in 60 hours 1/2 1/2 1/2 1/2

Half-Life Calculation #1 You have 400 mg of a radioisotope with a half-life of 5 minutes. How much will be left after 30 minutes?

Half-Life Calculation #2 Suppose you have a 100 mg sample of Au-191, which has a half-life of 3.4 hours. How much will remain after 10.2 hours?

Half-Life Calculation # 3 Cobalt-60 is a radioactive isotope used in cancer treatment. Co-60 has a half-life of 5 years. If a hospital starts with a 1000 mg supply, how many mg will need to be purchased after 10 years to replenish the original supply?

Answers to Half-Life Calculations 6.25 mg Half-Life Calculation #2 12.5 mg Half-Life Calculation #3 750 mg

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. The half life of carbon-14 is 5730 years 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