# CHAPTER 20 Nuclear Chemistry and Radioactivity 20.3 Rate of Radioactive Decay

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<p>CHAPTER 20 Nuclear Chemistry and Radioactivity 20.3 Rate of Radioactive Decay Slide 2 2 What is carbon dating? How can we tell how old fossils are? Slide 3 3 20.3 Rate of Radioactive Decay What is carbon dating? How can we tell how old fossils are? We introduce the time variable Reaction rates Slide 4 4 20.3 Rate of Radioactive Decay What is carbon dating? How can we tell how old fossils are? We introduce the time variable In Chapter 12 we studied reaction rates for chemical reactions Nuclear reactions also involve rates! Reaction rates Slide 5 5 20.3 Rate of Radioactive Decay Some reactions take place very quickly; they have a short half-life, t 1/2. half-life: the time it takes for half of the atoms in a sample to decay. Decay Slide 6 6 20.3 Rate of Radioactive Decay Half-life Slide 7 7 20.3 Rate of Radioactive Decay Half-life Every radioactive isotope has a different half-life. Isotopes with short half-lives do not occur in nature, but must be generated in the laboratory. Slide 8 8 20.3 Rate of Radioactive Decay Carbon dating Carbon dating revolves around carbon-14, a radioactive isotope. Carbon-14 is generated in the upper atmosphere through a bombardment reaction: Neutrons generated by cosmic rays becomes 14 CO 2 in the atmosphere Slide 9 9 20.3 Rate of Radioactive Decay Carbon-14 goes through the same cycle as carbon-12 Carbon dating 14 Slide 10 10 20.3 Rate of Radioactive Decay In living organisms: Carbon dating This ratio stays constant while the organism is alive Slide 11 11 20.3 Rate of Radioactive Decay In living organisms: Carbon dating Over time, carbon-14 decays by emission: This ratio stays constant while the organism is alive Slide 12 12 20.3 Rate of Radioactive Decay Over time, carbon-14 decays by emission: Carbon dating When the organism dies, it no longer consumes carbon from the environment. The number of carbon-14 atoms in the dead organism will decrease over time. Slide 13 13 20.3 Rate of Radioactive Decay Carbon dating Ratio not to scale An archeologist looks at the ratio of carbon-14 to carbon-12. Carbon dating works reliably up to about 10 times the half-life, or 57,300 years (beyond that time, there is not enough carbon-14 left to detect accurately). Carbon dating only works on material that has once been living: tissue, bone, or wood. Slide 14 14 20.3 Rate of Radioactive Decay About 18% of the mass of a live animal is carbon. If 1 g of live bone contains about 90 billion carbon-14 atoms (t 1/2 = 5,730 years), how many C-14 atoms remain in 1 g of bone 17,190 years after the animal dies? Slide 15 15 20.3 Rate of Radioactive Decay About 18% of the mass of a live animal is carbon. If 1 g of live bone contains about 90 billion carbon-14 atoms (t 1/2 = 5,730 years), how many C-14 atoms remain in 1 g of bone 17,190 years after the animal dies? Given:The half-life and the number of carbon-14 atoms Slide 16 16 20.3 Rate of Radioactive Decay About 18% of the mass of a live animal is carbon. If 1 g of live bone contains about 90 billion carbon-14 atoms (t 1/2 = 5,730 years), how many C-14 atoms remain in 1 g of bone 17,190 years after the animal dies? Given:The half-life and the number of carbon-14 atoms Solve:Since 17,190 years is three half-lives, the initial amount must be reduced by a factor of 2 x 2 x 2 = 8. 90 billion / 8 = 11.25 billion Slide 17 17 20.3 Rate of Radioactive Decay About 18% of the mass of a live animal is carbon. If 1 g of live bone contains about 90 billion carbon-14 atoms (t 1/2 = 5,730 years), how many C-14 atoms remain in 1 g of bone 17,190 years after the animal dies? Given:The half-life and the number of carbon-14 atoms Solve:Since 17,190 years is three half-lives, the initial amount must be reduced by a factor of 2 x 2 x 2 = 8. 90 billion / 8 = 11.25 billion Answer:After three half-lives the amount of carbon-14 atoms is reduced by a factor of 8, from 90 billion to 11.25 billion. Slide 18 18 20.3 Rate of Radioactive Decay Every radioactive isotope has a different half-life, t 1/2 Carbon dating is based on the knowledge that t 1/2 for carbon-14 is 5,730 years Ratio not to scale Slide 19 19 20.3 Rate of Radioactive Decay Rate of decay The number of nuclei in the sample (N) is constant A short half-life implies a large rate constant, k. Slide 20 20 20.3 Rate of Radioactive Decay Rate of decay Carbon-14 and radium-220 have half-lives of 5,730 years and 1 minute, respectively. Calculate the rate constants for their decay, in units of 1/s. Slide 21 21 20.3 Rate of Radioactive Decay Rate of decay Carbon-14 and radium-220 have half-lives of 5,730 years and 1 minute, respectively. Calculate the rate constants for their decay, in units of 1/s. Asked:The rate constant k Given:The half-life t 1/2 for each radioactive decay process. Relationships:The equation that relates t 1/2 to k: k = 0.693 / t 1/2 Slide 22 22 20.3 Rate of Radioactive Decay Rate of decay Carbon-14 and radium-220 have half-lives of 5,730 years and 1 minute, respectively. Calculate the rate constants for their decay, in units of 1/s. Asked:The rate constant k Given:The half-life t 1/2 for each radioactive decay process. Relationships:The equation that relates t 1/2 to k: k = 0.693 / t 1/2 Solve:For C-14, t 1/2 = 5,730 years, and. Slide 23 23 20.3 Rate of Radioactive Decay Rate of decay Carbon-14 and radium-220 have half-lives of 5,730 years and 1 minute, respectively. Calculate the rate constants for their decay, in units of 1/s. Asked:The rate constant k Given:The half-life t 1/2 for each radioactive decay process. Relationships:The equation that relates t 1/2 to k: k = 0.693 / t 1/2 Solve:For C-14, t 1/2 = 5,730 years, and For Ra-220, t 1/2 = 1 min, and Slide 24 24 20.3 Rate of Radioactive Decay Rate of decay Carbon-14 and radium-220 have half-lives of 5,730 years and 1 minute, respectively. Calculate the rate constants for their decay, in units of 1/s. Asked:The rate constant k Given:The half-life t 1/2 for each radioactive decay process. Relationships:The equation that relates t 1/2 to k: k = 0.693 / t 1/2 Solve:For C-14, t 1/2 = 5,730 years, and For Ra-220, t 1/2 = 1 min, and Discussion:Note that a small t 1/2 gives a large k. The rate constant k gives us an indication of the number of decays over a certain period of time. Slide 25 25 20.3 Rate of Radioactive Decay Decay rate law The rate of decay of a radioactive sample is also called the activity of the sample Slide 26 26 20.3 Rate of Radioactive Decay Decay rate law Plutonium-236 decays by emitting an alpha particle and has a half-life of 2.86 years. If we start with 10 mg of Pu-236, how much remains after 4 years? Slide 27 27 20.3 Rate of Radioactive Decay Decay rate law Plutonium-236 decays by emitting an alpha particle and has a half-life of 2.86 years. If we start with 10 mg of Pu-236, how much remains after 4 years? Asked:N, the amount left after 4 years Given:The half-life t 1/2, the initial amount N 0, and the elapsed time t Relationships:The equation that relates t 1/2 and N 0 to N is Slide 28 28 20.3 Rate of Radioactive Decay Decay rate law Plutonium-236 decays by emitting an alpha particle and has a half-life of 2.86 years. If we start with 10 mg of Pu-236, how much remains after 4 years? Asked:N, the amount left after 4 years Given:The half-life t 1/2, the initial amount N 0, and the elapsed time t Relationships:The equation that relates t 1/2 and N 0 to N is Solve: Slide 29 29 20.3 Rate of Radioactive Decay Decay rate law Plutonium-236 decays by emitting an alpha particle and has a half-life of 2.86 years. If we start with 10 mg of Pu-236, how much remains after 4 years? Asked:N, the amount left after 4 years Given:The half-life t 1/2, the initial amount N 0, and the elapsed time t Relationships:The equation that relates t 1/2 and N 0 to N is Solve: Discussion:After 4 years, the initial 10 mg is reduced to 3.79 mg, which is 37.9% of the initial amount of Pu-236. Slide 30 30 20.3 Rate of Radioactive Decay Radioactive dating the composition of the atmosphere over time the age of rocks that are billions of years old the age of a once-living organism Information can be extracted from the ratio of specific isotopes Carbon-14 and carbon-12 Oxygen-18 and oxygen-16 Uranium-238 and plutonium-239 Slide 31 31 20.3 Rate of Radioactive Decay Radioactive dating The amount of sample remaining, compared to the initial amount of sample, can be used to determine the age of the sample. Slide 32 32 20.3 Rate of Radioactive Decay An ancient Greek scroll written on an animal skin was discovered by archeologists in 2008. They isolated 10 g of it and measured the carbon-14 decay rate to be 111 disintegrations/minute. Calculate the age of the scroll. (Assume that living organisms have a carbon-14 decay rate of 15 disintegrations per minute per gram of C.) Slide 33 33 20.3 Rate of Radioactive Decay An ancient Greek scroll written on an animal skin was discovered by archeologists in 2008. They isolated 10 g of it and measured the carbon-14 decay rate to be 111 disintegrations/minute. Calculate the age of the scroll. (Assume that living organisms have a carbon-14 decay rate of 15 disintegrations per minute per gram of C.) Given:The initial decay rate of C-14: N 0 = 15 disintegrations/(ming). The present decay rate of C-14 is 11 disintegrations/(ming). The half-life of C-14 is 5,730 years. Slide 34 34 20.3 Rate of Radioactive Decay An ancient Greek scroll written on an animal skin was discovered by archeologists in 2008. They isolated 10 g of it and measured the carbon-14 decay rate to be 111 disintegrations/minute. Calculate the age of the scroll. (Assume that living organisms have a carbon-14 decay rate of 15 disintegrations per minute per gram of C.) Given:The initial decay rate of C-14: N 0 = 15 disintegrations/(ming). The present decay rate of C-14 is 11 disintegrations/(ming). The half-life of C-14 is 5,730 years. Solve:For the rate constant k: Slide 35 35 20.3 Rate of Radioactive Decay An ancient Greek scroll written on an animal skin was discovered by archeologists in 2008. They isolated 10 g of it and measured the carbon-14 decay rate to be 111 disintegrations/minute. Calculate the age of the scroll. (Assume that living organisms have a carbon-14 decay rate of 15 disintegrations per minute per gram of C.) Given:The initial decay rate of C-14: N 0 = 15 disintegrations/(ming). The present decay rate of C-14 is 11 disintegrations/(ming). The half-life of C-14 is 5,730 years. Solve:For the rate constant k: And the time is: Slide 36 36 20.3 Rate of Radioactive Decay An ancient Greek scroll written on an animal skin was discovered by archeologists in 2008. They isolated 10 g of it and measured the carbon-14 decay rate to be 111 disintegrations/minute. Calculate the age of the scroll. (Assume that living organisms have a carbon-14 decay rate of 15 disintegrations per minute per gram of C.) Given:The initial decay rate of C-14: N 0 = 15 disintegrations/(ming). The present decay rate of C-14 is 11 disintegrations/(ming). The half-life of C-14 is 5,730 years. Solve:For the rate constant k: And the time is: Discussion:The animal skin on which the scroll was written was 2,491 years old. It was written in about 483 BC. Slide 37 37 20.3 Rate of Radioactive Decay Mathematics of radioactive decay </p>

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