Half-Life.

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Presentation transcript:

Half-Life

Half-Life 20 g 10 g 5 g 2.5 g after 1 half-life after 2 half-lives Start Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 757

Half-Life g I Xe b- 1.00 mg 0.875 mg 0.500 mg 0.750 mg Xe 0.500 mg I I b emissions g emissions 89.9% 7.3% 131 53 I 54 Xe Xe* Half-Life 1.00 mg 0.875 mg 0.500 mg 0.750 mg 131 54 Xe 131 53 0.500 mg I 131 53 I 0.250 mg http://images.google.com/imgres?imgurl=http://www.ehs.utoronto.ca/Assets/ehs3/radtraining/K42decay.gif.gif&imgrefurl=http://www.ehs.utoronto.ca/services/radiation/radtraining/nuclideinformation.htm&h=182&w=300&sz=2&hl=en&start=19&tbnid=nb4ytTa7sUkp-M:&tbnh=70&tbnw=116&prev=/images%3Fq%3Diodine-131%2Bdecay%26start%3D18%26gbv%3D2%26ndsp%3D18%26hl%3Den%26sa%3DN 0.125 mg 8.02 days 16.04 days 24.06 days 0.00 days I 131 53 Xe 54 b- -1 + g Dorin, Demmin, Gabel, Chemistry The Study of Matter 3rd Edition, page 757

Half-life of Radiation Initial amount of radioisotope 0 1 2 3 4 Number of half-lives Radioisotope remaining (%) 100 50 25 12.5 After 1 half-life After 2 half-lives After 3 half-lives t1/2 t1/2 t1/2

Half-Life Plot Half-life of iodine-131 is 8 days 20 Half-life of iodine-131 is 8 days 15 1 half-life Amount of Iodine-131 (g) 10 16 2 half-lives 5 24 3 half-lives 32 4 half-lives etc… 40 48 56 8 Time (days) Timberlake, Chemistry 7th Edition, page 104

Half-Life of Isotopes Half-Life and Radiation of Some Naturally Occurring Radioisotopes Isotope Half-Live Radiation emitted Carbon-14 5.73 x 103 years b Potassium-40 1.25 x 109 years b, g Radon-222 3.8 days a Radium-226 1.6 x 103 years a, g Thorium-230 7.54 x 104 years a, g Thorium-234 24.1 days b, g Uranium-235 7.0 x 108 years a, g Uranium-238 4.46 x 109 years a

Half-life (t½) Time required for half the atoms of a radioactive nuclide to decay. Shorter half-life = less stable. 1/2 1/4 1/8 1/16 1/1 1/2 1/4 1/8 1/16 Ratio of Remaining Potassium-40 Atoms to Original Potassium-40 Atoms 1 half-life 1.3 1 half-lives 2.6 3 half-lives 3.9 5.2 Time (billions of years) Newly formed rock Potassium Argon Calcium

Half-life (t½) Time required for half the atoms of a radioactive nuclide to decay. Shorter half-life = less stable. 1/1 Newly formed rock Potassium Argon Calcium Ratio of Remaining Potassium-40 Atoms to Original Potassium-40 Atoms 1/2 1/4 1/8 1/16 1 half-life 1.3 1 half-lives 2.6 3 half-lives 3.9 1 half-lives 5.2 Time (billions of years)

Copyright © Pearson Education, Inc., publishing as Benjamin Cummings

How Much Remains? After one half-life, of the original atoms remain. 1 2 After two half-lives, ½ x ½ = 1/(22) = of the original atoms remain. 1 4 After three half-life, ½ x ½ x ½ = 1/(23) = of the original atoms remain. 1 8 After four half-life, ½ x ½ x ½ x ½ = 1/(24) = of the original atoms remain. 1 16 After five half-life, ½ x ½ x ½ x ½ x ½ = 1/(25) = of the original atoms remain. 1 32 After six half-life, ½ x ½ x ½ x ½ x ½ x ½ = 1/(26) = of the original atoms remain. 1 64 Accumulating “daughter” isotopes 1 2 1 4 Surviving “parent” isotopes 1 8 1 16 1 32 1 64 1 128 Beginning 1 half-life 2 half-lives 3 half-lives 4 half-life 5 half-lives 6 half-lives 7 half-lives

2. The burning creates carbon dioxide gas comprised of carbon-12 1. A small piece of fossil is burned in a special furnace. 2. The burning creates carbon dioxide gas comprised of carbon-12 isotopes and carbon-14 isotopes. Stable C-12 isotope Nitrogen Decaying C-14 isotope 3. As the carbon- 14 decays into nitrogen-14, it emits an electron. Electron http://www.signonsandiego.com/uniontrib/20070628/images/curr-carbon430.gif All organisms absorb, use and accumulate the element carbon during life. There are several types or isotopes, depending upon the number of neutrons in the carbon atom. It is the difference in the behavior of these isotopes that permits researchers to estimate age. While alive, organisms accumulate both carbon-12 and carbon-14 isotopes at a steady ratio of about 12 trillion C-12 isotopes to each C-14 isotope. Carbon-12 is a stable isotope. It doesn't change or decay. A fossil or piece of parchment contains as much C-12 as the original living dinosaur or goat. In contrast, C-14 is radioactive. It is always in a process of decay, with a half-life of 5,730 years. That means that after 5,730 years, only half of the original C-14 in an organic sample will remain, the rest having decayed into another element, specifically nitrogen-14. By measuring the ratio of C-12 to remaining C-14 atoms in a sample and comparing it to the known rate of C-14 decay, researchers can estimate the age of almost any organic object. 4. A radiation counter records the number of electrons emitted. Note: Not to scale. SOURCE: Collaboration for NDT Education MATT PERRY / Union-Tribune

The iodine-131 nuclide has a half-life of 8 days The iodine-131 nuclide has a half-life of 8 days. If you originally have a 625-g sample, after 2 months you will have approximately? 40 g 20 g 10 g 5 g less than 1 g Data Table: Half-life Decay ~ Amount Time # Half-Life 625 g 312 g 156 g 78 g 39 g 20 g 10 g 5 g 2.5 g 1.25 g 0 d 8 d 16 d 24 d 32 d 40 d 48 d 56 d 64 d 72 d 1 2 3 4 5 6 7 8 9 N = No(1/2)n N = amount remaining No = original amount n = # of half-life(s) N = (625 g)(1/2)7.5 Assume 30 days = 1 month N = 3.45 g 60 days = 7.5 half-life(s) 8 days

N ln = - k t No 0.693 ln 2 t1/2 = k 0.693 k 1.5 g k = 1.209 x 10-4 Given that the half-life of carbon-14 is 5730 years, consider a sample of fossilized wood that, when alive, would have contained 24 g of carbon-14. It now contains 1.5 g of carbon-14. How old is the sample? Data Table: Half-life Decay ln = - k t N No Amount Time # Half-Life 24 g 12 g 6 g 3 g 1.5 g 0 y 5,730 y 11,460 y 17,190 y 22,920 y 1 2 3 4 0.693 ln 2 t1/2 = k 0.693 Petrified wood is a type of fossil: it exists of fossil wood where all the organic materials have been replaced with minerals (most often a silicate, such as quartz), while retaining the original structure of the wood. http://upload.wikimedia.org/wikipedia/commons/thumb/f/f3/PetrifiedWood.jpg/180px-PetrifiedWood.jpg 5730 y = k ln = - (1.209x10-4) t 1.5 g 24 g k = 1.209 x 10-4 t = 22,933 years

Half-Life Practice Calculations The half-life of carbon-14 is 5730 years. If a sample originally contained 3.36 g of C-14, how much is present after 22,920 years? Gold-191 has a half-life of 12.4 hours. After one day and 13.2 hours, 10.6 g of gold-19 remains in a sample. How much gold-191 was originally present in the sample? There are 3.29 g of iodine-126 remaining in a sample originally containing 26.3 g of iodine-126. The half-life of iodine-126 is 13 days. How old is the sample? A sample that originally contained 2.5 g of rubidium-87 now contains 1.25 g. The half-life of rubidium-87 is 6 x 1010 years. How old is the sample? Is this possible? Why or why not? 0.21 g C-14 84.8 g Au-191 39 days old 6 x 1010 years (60,000,000,000 billions years old) What is the age of Earth??? Demo: Try to cut a string in half seven times (if it begins your arms length).

3.36 g of C-14, how much is present after 22,920 years? The half-life of carbon-14 is 5730 years. If a sample originally contained 3.36 g of C-14, how much is present after 22,920 years? Data Table: Half-life Decay t1/2 = 5730 years Amount Time # Half-Life 3.36 g 1.68 g 0.84 g 0.42 g 0.21 g 0 y 5,730 y 11,460 y 17,190 y 22,920 y 1 2 3 4 22,930 years n = 5,730 years n = 4 half-life http://www.abc.net.au/reslib/200410/r34321_85394.jpg Australian scientists have found a new species of hobbit-sized humans who lived about 18,000 years ago on an Indonesian island. The discovery adds another piece to the complex puzzle of human evolution. The partial skeleton of Homo floresiensis, found in a cave on the island of Flores, is of an adult female that was a meter tall, had a chimpanzee-sized brain and was substantially different from modern humans. It shared the isolated island to the east of Java with miniature elephants and Komodo dragons. The hominins walked upright and probably evolved into their dwarf size because of environmental conditions and coexisted with modern humans in the region for thousands of years. (# of half-life)(half-life) = age of sample (4 half-life)(5730 years) = age of sample 22,920 years

Half-life Half-life worksheet