Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Chapter 9 Nuclear Radiation 9.4 Half-Life of a Radioisotope 1
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Half-Life and Decay Curves The half-life of a radioisotope is the time for the radiation level to decrease (decay) to one-half of the original value. 2 The decay curve for I-131 shows that one-half the sample decays every 8 days.
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Half-Lives of Some Radioisotopes 3
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Guide to Using Half-Lives 4
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Half-Life Calculations The radioisotope strontium-90 has a half-life of 38.1 years. If a sample contains 36 mg of Sr-90, how many milligrams will remain after years? Step 1State the given and needed quantities. Given: 36 mg, years, half-life of 38.1 years Needed: mg Sr-90 remaining Step 2Write a plan to calculate unknown quantity. Half-life years number of half-lives Number of half-lives 36 mg Sr-90 mg Sr-90 remaining 5
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Half-Life Calculations The radioisotope strontium-90 has a half-life of 38.1 years. If a sample contains 36 mg of Sr-90, how many milligrams will remain after years? Step 3 Write the half-life equality and conversion factors. 1 half-life = 38.1 years 38.1 years and 1 half-life 1 half-life 38.1 years 6
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Half-Life Calculations The radioisotope strontium-90 has a half-life of 38.1 years. If a sample contains 36 mg of Sr-90, how many milligrams will remain after years? Step 4 Set up the problem to calculate amount of active radioisotope. Number of half-lives 4 years x 1 half-life = 4 half-lives 38.1 years 1 half-life 2 half-lives 3 half-lives 4 half-lives 36 mg 18 mg 9 mg 4.5 mg 2.3 mg Sr-90 7
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check Carbon-14 was used to determine the age of the Dead Sea Scrolls. If the Dead Sea Scrolls were determined to be 2000 years old and the half-life of carbon-14 is 5730 years, what fraction of this half-life has passed? 8
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution Carbon-14 was used to determine the age of the Dead Sea Scrolls. If the Dead Sea Scrolls were determined to be 2000 years old and the half-life of carbon-14 is 5730 years, what fraction of this half-life has passed? 2000 years x 1 half-life = 0.35 half-life 5730 years 9
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Learning Check The half-life of I-123 is 13 h. How much of a 64-mg sample of I-123 is left after 26 hours? A. 32 mg B. 16 mg C. 8 mg 10
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution The half-life of I-123 is 13 h. How much of a 64-mg sample of I-123 is left after 26 hours? Step 1State the given and needed quantities. Given: 64 mg, 26 hours, half-life of 13 hours Needed: mg I-123 remaining Step 2Write a plan to calculate unknown quantity. Half-life 26 hours number of half-lives Number of half-lives 64 mg I-123 mg I-123 remaining 11
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution The half-life of I-123 is 13 h. How much of a 64-mg sample of I-123 is left after 26 hours? Step 3Write the half-life equality and conversion factors. 1 half-life = 13 hours 13 hours and 1 half-life 1 half-life 13 hours 12
Chemistry: An Introduction to General, Organic, and Biological Chemistry, Eleventh Edition Copyright © 2012 by Pearson Education, Inc. Solution The half-life of I-123 is 13 h. How much of a 64-mg sample of I-123 is left after 26 hours? Step 4Set up the problem to calculate amount of active radioisotope. Number of half-lives 26 hours x 1 half-life = 2 half-lives 13 hours 1 half-life 2 half-lives 64 mg 32 mg 16 mg I-123 The answer is B, 16 mg of I-123 remain. 13