--- title: "How long does radioactivity last?" subtitle: "Years 9 and 10 Chemistry · Inside the atom · Lesson 4" --- # How long does radioactivity last? **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Doctors give patients a radioactive drug in the morning that is almost gone by the next day. Yet some uranium in the rocks under you was made before the Earth formed, and about half of it is still there. :::teacher-note **In one sentence:** Students define half-life, work out how much of a sample is left after a number of half-lives, explain that decay is random for one nucleus but predictable for many, and link half-life to uses (AC9S9U06, node 4). **Students should be able to say:** I can define half-life. I can work out how much of a sample is left after a number of half-lives. I can explain why an isotope's half-life suits a use. **Width:** the unmarked parts are the floor every student does (Engage, Explore, Explain, Evaluate). Typical and Wider sections add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Engage :::keep-together **A sample has 80 iodine-131 nuclei. Half of any sample decays in 8 days. How many are left after 16 days?** ☐ 20 ☐ 40 ☐ 60 ☐ 0: two halves make a whole My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** About 20. In the first 8 days half of the 80 go, leaving 40. In the next 8 days half of those 40 go, leaving 20. It halves each time; it never takes the same number twice. ::: ## Explore Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Explain: half-life :::keep-together ### What half-life is **What is the half-life of a radioactive isotope?** ☐ The time for half the nuclei in a sample to decay ☐ The time for one nucleus to decay halfway ☐ Half the time it takes the whole sample to decay ::: :::teacher-note **Answer:** The time for half the nuclei in a sample to decay The half-life is the time for half the nuclei in a sample to decay. It is the same however big the sample is and however long it has been decaying. ::: :::keep-together ### Three half-lives **A sample starts with 800 nuclei. How many are left after 3 half-lives?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 100 800 → 400 → 200 → 100. After 3 half-lives, an eighth is left. ::: :::keep-together ### Carbon-14 **Carbon-14 has a half-life of 5730 years. How many years until a quarter of a sample is left?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 11460 A quarter is left after 2 half-lives: 2 × 5730 = 11 460 years. ::: :::keep-together ### One nucleus **You watch one carbon-14 nucleus. When will it decay?** ☐ Within 5730 years for certain ☐ In exactly 5730 years ☐ No one can say: it could be in a second or in 50 000 years ::: :::teacher-note **Answer:** No one can say: it could be in a second or in 50 000 years Decay is random for each nucleus. Only for a large sample can we say how many will go in a given time. ::: :::keep-together ### Nothing changes it **A sample is heated, crushed and dissolved in acid. What happens to its half-life?** ☐ Nothing: half-life is the same whatever you do to the sample ☐ It gets shorter ☐ It gets longer ::: :::teacher-note **Answer:** Nothing: half-life is the same whatever you do to the sample Half-life is a property of the nucleus. Temperature, pressure and chemical reactions change the electrons around it, not the nucleus. ::: :::typical ## Elaborate: fluorine-18 in hospitals :::keep-together ### After 330 minutes **Fluorine-18 has a half-life of 110 minutes. What percentage of it is left 330 minutes after it is made?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 12.5 330 minutes is 3 half-lives: 100% → 50% → 25% → 12.5%. ::: :::keep-together ### Why 2 hours **Fluorine-18 is used in PET scans: it is made in the hospital, injected, and its radiation is detected outside the body. Why does a half-life of about 2 hours suit this?** ☐ Any half-life would do: it makes no difference ☐ So the patient stays radioactive for years, ready for the next scan ☐ Long enough to make, inject and scan, short enough that little is left in the body by the next day ::: :::teacher-note **Answer:** Long enough to make, inject and scan, short enough that little is left in the body by the next day After a day (about 13 half-lives) less than a thousandth is left. Isotopes for dating rocks, by contrast, need half-lives of millions or billions of years. ::: ::: :::wider ## Elaborate: dating the past :::keep-together ### An old fireplace **Charcoal from an old fireplace has an eighth of the carbon-14 that living wood has. Carbon-14's half-life is 5730 years. About how old is it, in years?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 17190 An eighth is left after 3 half-lives: 3 × 5730 = 17 190 years. ::: :::keep-together ### The limit **Radiocarbon dating works back to about 50 000 years. Why not further?** ☐ After about 9 half-lives less than a five-hundredth of the carbon-14 is left, too little to measure reliably ☐ Nothing older than 50 000 years contains carbon ☐ Carbon-14 stops decaying after 50 000 years ::: :::teacher-note **Answer:** After about 9 half-lives less than a five-hundredth of the carbon-14 is left, too little to measure reliably Each half-life halves what is left: after 9 half-lives (about 52 000 years) less than 0.2% remains, and tiny traces of modern carbon would swamp it. ::: :::keep-together ### More than 60 000 years **Sites in northern Australia show First Peoples were there more than 60 000 years ago. Radiocarbon dates the younger layers; older layers are dated by other methods, such as luminescence (when sand grains were last in sunlight). Why does using more than one method matter?** ☐ Radiocarbon is always wrong ☐ It doesn't: one method is enough ☐ Independent methods that agree make the dates much more trustworthy ::: :::teacher-note **Answer:** Independent methods that agree make the dates much more trustworthy Where their ranges overlap the methods are checked against each other, and agreement between independent methods is strong evidence. Together with First Peoples' own knowledge of Country, they show people have lived in Australia for more than 60 000 years. ::: ::: ## Evaluate: look back Write one sentence: "At first I thought… Now I think… because…" **Revision summary** - Each unstable nucleus decays at random: no one can say which will go next, or when. - A large sample decays in a predictable way: half of it goes in one **half-life**, half of what is left in the next, and so on (1/2, 1/4, 1/8 …). - Half-life is a property of the isotope; heat, pressure and chemical reactions don't change it. - Short half-lives suit medical imaging (fluorine-18, about 2 hours); long ones suit dating (carbon-14, 5730 years; uranium-238, 4.5 billion years). ## Exit ticket :::keep-together **Iodine-131 has a half-life of 8 days. A hospital receives 40 g. How much is left after 24 days?** {{lines-3}} ::: :::teacher-note **Answer:** 5 g (40 → 20 → 10 → 5: three half-lives). :::