General, Organic, and Biological Chemistry Fourth Edition Karen Timberlake 4.4 Half-life of a Radioisotope Chapter 4 Nuclear Chemistry © 2013 Pearson Education, Inc. Lectures

© 2013 Pearson Education, Inc. Chapter 4, Section 4 2 Half-life The half-life of a radioisotope is the time for the radiation level to decrease (decay) to one-half of the original value.

© 2013 Pearson Education, Inc. Chapter 4, Section 4 3 Decay Curve A decay curve shows the decay of radioactive atoms and the remaining radioactive sample.

© 2013 Pearson Education, Inc. Chapter 4, Section 4 4  In one half-life, 40 mg of a radioisotope decays to 20 mg.  After two half-lives, 10 mg of a radioisotope remain. Initial 40 mg 20 mg 10 mg Half-life Calculations 1 half-life 2 half-lives

© 2013 Pearson Education, Inc. Chapter 4, Section 4 5 Guide to Calculating Half-lives

© 2013 Pearson Education, Inc. Chapter 4, Section 4 6 Sample Calculation of Half-lives P-32, a radioisotope used to treat leukemia, has a half- life of 14.3 days. If a sample contains 8.0 mg of P-32, how many milligrams of P-32 remain after 42.9 days? Step 1 State the given and needed quantities. Analyze the Problem. GivenNeed 8.0 mg of P-32 half-life of 14.3 days 42.9 days elapsedmilligrams of P-32 remaining

© 2013 Pearson Education, Inc. Chapter 4, Section 4 7 Sample Calculation of Half-lives P-32, a radioisotope used to treat leukemia, has a half- life of 14.3 days. If a sample contains 8.0 mg of P-32, how many milligrams of P-32 remain after 42.9 days? Step 2 Write a plan to calculate the unknown quantity. half-life number of half-lives daysnumber of half-lives milligrams of milligrams remaining

© 2013 Pearson Education, Inc. Chapter 4, Section 4 8 Sample Calculation of Half-lives P-32, a radioisotope used to treat leukemia, has a half- life of 14.3 days. If a sample contains 8.0 mg of P-32, how many milligrams of P-32 remain after 42.9 days? Step 3 Write the half-life equality and conversion factors.

© 2013 Pearson Education, Inc. Chapter 4, Section 4 9 Sample Calculation of Half-lives P-32, a radioisotope used to treat leukemia, has a half- life of 14.3 days. If a sample contains 8.0 mg of P-32, how many milligrams of P-32 remain after 42.9 days? Step 4 Set up the problem to calculate the needed quantity.

© 2013 Pearson Education, Inc. Chapter 4, Section 4 10 Half-Lives of Some Radioisotopes Radioisotopes that are  naturally occurring tend to have long half-lives.  used in nuclear medicine have short half-lives.

© 2013 Pearson Education, Inc. Chapter 4, Section 4 11 The half life of I-123 is 13 hours. How much of a 64-mg sample of I-123 remains active after 26 hours? A. 32 mg B. 16 mg C. 8 mg Learning Check

© 2013 Pearson Education, Inc. Chapter 4, Section 4 12 The half life of I-123 is 13 hours. How much of a 64-mg sample of I-123 remains active after 26 hours? Step 1 State the given and needed quantities. Analyze the Problem. Solution

© 2013 Pearson Education, Inc. Chapter 4, Section 4 13 The half life of I-123 is 13 hours. How much of a 64-mg sample of I-123 remains active after 26 hours? Step 2 Write a plan to calculate the unknown quantity. Solution 26 h number of half-lives 64 g amount remaining half-life number of half-lives

© 2013 Pearson Education, Inc. Chapter 4, Section 4 14 The half life of I-123 is 13 hours. How much of a 64-mg sample of I-123 remains active after 26 hours? Step 3 Write the half-life equality and conversion factors. Solution

© 2013 Pearson Education, Inc. Chapter 4, Section 4 15 The half life of I-123 is 13 hours. How much of a 64-mg sample of I-123 remains active after 26 hours? Step 4 Set up the problem to calculate the needed quantity. Solution Answer: B