Question

MODELING RADIOACTIVE DECAY WITH PENNIES ADVANCED STUDY ASSIGNMENT MODEL 2: RADIONUCLIDE HALF-LIFE The time required for half of a sample of a radionuclides (radioactive isotopes) to decay is called the half-life (units of time). Table 2 below illustrates the half-lives of several radioisotopes and the Table 2: Half-lives of some Radioisoto barium-131 carbon-14 chromium-51 cobalt-60 iodine-131 uranium-238 Radiation Half-life 11.6 days 5730 yrs 27.8 days 5.3 yrs 8.1 days 4.47. 109 yr Application detection of bone tumors carbon dating measuring blood volume food irradiation, cancer therapy y, X-rays dating igneous rocks Critical Thinking Questions: 10. Consider a 100-gram sample of radioactive cobalt-60. a. How much time will it take before half the sample has decayed? b. Approximately how many grams of radioactive cobalt-60 will remain after 11 years? 11. Consider a sample of iodine-131 How many half-lives would it take for the sample to decay until less than 1% of the original isotope remained? a. b. How many days would this take? 8 of 8
Modeling radioactive decay in pennies

Answer 1

(a) It takes 5.3 years before half the sample has decreased (b) we have t_1/2 = 0.693/K & K = 0.693/t_1/2 for cobalt 60 t_1/2 = 5.3 years Therefore K = 0.693/5.3 K = 0.130 year we know radioactive decovy follows 1^st order Konetics k = 2.303/t log (a/a -x) a = initial concentration = 100 (a - x) = Remained Co - 60 \r\n t = 11 years K = 0.130 Therefore 0.130 = 2.303/11 log (100/100 - x) ( 11 times 0.130)/2.303 = log (100/100- x) log (100/100 - x) = 0.6245 100/100 - x = 4.212 (100 - x) = 100/4.212 = 23.739 x = 100 - 23.739 x = 76.26 100 - 76.26 = 23.739 g Therefore 23.739 g of cobalt 60 remains after 11 years \r\n 100 rightarrow 50 rightarrow 25 rightarrow 12.5 rightarrow 6.25 rightarrow 3.125 rightarrow 1.5625 rightarrow 0.78125 Iodine 131 takes 7 half lives to remain less than 1 % of original amount (b) If one half life of I^131 = 8.1 then 7 half lives will be = 7 times 8.1 = 56.7 days
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