Dividing by 2 10/15/2015. Unit 3: Atomic Structure - The Nucleus Lesson 3.5: Half-Life 99

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1 /15/2015 Dividing by 2 Unit 3: Atomic Structure - The Nucleus Lesson 3.5: Half-Life 99 The Random Nature of the Universe Quantum mechanics says that it is impossible to know when any particular atom is going to do anything. However, It is quite possible to know how many of a large number of atoms will do something. This might not make sense to you (like many other things in quantum mechanics), but it is true. 0 Radioactive Decay An unstable nucleus emitting radiation follows the rules on the previous slide. We can not know when any particular nucleus will decay. But... We can know how long it will take for ½ of a sample of many nuclei to decay. This is called half-life life 1 1

2 /15/2015 Half lifelife Half-life (for radioisotopes): The time it takes for half of the nuclei in a sample of radioactive materials to decay. Half-life for a specific radioisotope is constant. It won t ever change. The half-lives of some radioisotopes are listed on Reference Table N 2 Q: How many half-lives will it take for a particular sample of radioactive material to completely decay? A: It is impossible to say. IT IS NEVER, EVER 2 (unless your sample consisted of 2 atoms). 3 Radioactive Decay Rates (cont.) 4 2

3 /15/ Different Types of Half-Life Problems Type 1: You know how much of the isotope you have now, you want to find out how much will be left after a certain amount of time (going into the future). Step 1- Determine how many half lives will occur in the amount of time in the problem. Step 2- Divide the amount (mass, percent, fraction, number of atoms, etc.) by two as many times as there are half lives. 7 3

4 /15/ The half-life of Rn-222 (a carcinogenic house pollutant) is 3.8 days. If today your basement contains 20.0 grams of Rn-222, how much will remain after 19 days assuming no more pollutant leaks in? 8 2. A laboratory sample of 32 P triggers 400 clicks per minute in a Geiger-Mueller counter. How many days will it take for the 32 P to decay enough so that there are only 50 clicks per minute? (Hint: the number of clicks per minute represents the size mass of sample) 9 3. A cylinder contains 5.0 L of pure radioactive 19 Ne. If the cylinder is left to sit for 3.2 seconds, what percent of our original sample of 19 Ne will remain? 0 4

5 /15/2015 Type 2: You know how much of the isotope you have now, you want to find out how much there was a certain amount of time ago (going back in time to the past). Step 1- Determine how many half lives have gone by in the time span of the problem Step 2- Multiply the amount (mass, percent, fraction, number of atoms, etc.) by two as many times as there are half lives The half-life of Tc-99m* (used to locate brain tumors) is 6.0 hours. If 24 hours after admission. 0 micrograms are left, how much Tc-99m was administered originally? 2 2. A laboratory sample of 32 P triggers 0. clicks per minute in a Geiger-Mueller counter. How many days ago did the 32 P decayed enough to trigger clicks per minute? 3 5

6 /15/2015 Type 3: You want to find out how long the half-life is, knowing how much of a sample has decayed over a known period of time. Step 1- Determine how many times you need to cut your original amount in half to get your current amount. This is the number of half lives that have happened. Step 2- Divide the amount of time that has elapsed by the number of half lives A radioactive sample is placed next to a Geiger counter and monitored. In 20.0 hours, the counter s reading goes from 500 counts per minute to 125 counts per minute. How long is the half-life? 5 2. A sample of pure radioactive isotope is left to decay. After 40.0 days, the sample is placed in a mass spectrometer, and it is determined that the sample only 25% of the original isotope remains. How long is the half-life? 6 6

7 /15/2015 And for more advanced calculations: The amount of radioactive isotope remaining can be calculated: N is the remaining amount. N 0 is the initial amount. N is the remaining amount. N 0 is the initial amount. n is the number of half-lives that have passed. t is the elapsed time and T is the duration of the half-life. 7 Type 4: Radioactive Dating: The process of determining the age of an object by measuring the amount of certain isotopes is called radiochemical dating. In this process you are figuring out how many half- lives of a known radioisotope have occurred in the substance Carbon-dating is used to measure the age of artifacts that were once part of a living organism. 8 Radioactive dating (Cont...) What do we do? Step 1- Determine how many times you need to cut your original amount in half to get your final amount. This is the number of half lives that have happened. Step 2- Multiply the number of half-lives by the duration of the half-life for the isotope in the question (see Reference Table N) 9 7

8 /15/ The oldest rocks on Earth have been found to contain 50% U-238 and 50%Pb-206 (what U-238 ultimate decays into). What is the age of these rocks? An ancient scroll is discovered, and it is found that only 25% percent of the original concentration of C-14 (a radioactive isotope found in equal concentration in all living beings) remains. How old is the scroll? 12 1 Up and Atom! Any Questions? What now?