5.4 Half-Life of a Radioisotope The age of the Dead Sea Scrolls was determined using carbon-14. Learning Goal Given the half-life of a radioisotope, calculate the amount of radioisotope remaining after one or more half-lives.
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.
Decay Curves The decay curve for I-131 shows that one-half the sample decays every 8 days. The decay curve for iodine-131 shows that one-half of the radioactive sample decays and one-half remains radioactive after each half-life of 8 days. Core Chemistry Skill Using Half-Lives
Half-Lives of Some Radioisotopes
Guide to Using Half-Lives
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 152.4 years? STEP 1 State the given and needed quantities. ANALYZE Given Need THE PROBLEM 36 mg 152.4 yrs milligrams Sr-90 Sr-90 half-life = 38.1 yrs
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 152.4 years? STEP 2 Write a plan to calculate unknown quantity. years number of half-lives mg Sr-90 mg Sr-90 remaining Half-life Number of half-lives
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 152.4 years? STEP 3 Write the half-life equality and conversion factors.
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 152.4 years? STEP 4 Set up the problem to calculate the needed quantity. 1 half-life 2 half-lives 3 half-lives 4 half-lives 36 mg 18 mg 9 mg 4.5 mg 2.2 mg Sr-90
Study 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?
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? STEP 1 State the given and needed quantities. ANALYZE Given Need THE PROBLEM 2000 yrs old fraction of C-14 half-life = 5730 yrs half-life passed
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? STEP 2 Write a plan to calculate unknown quantity. years fraction of half-life STEP 3 Write the half-life equality and conversion factors. Half-life
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? STEP 4 Set up the problem to calculate the needed quantity.
Study 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
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 1 State the given and needed quantities. STEP 2 Write a plan to calculate unknown quantity. hours number of half-lives mg of I-123 mg of I-123 remaining ANALYZE Given Need THE PROBLEM 26 h 64 mg I-123 mg of I-123 I-123 half-life = 13 hours remaining Half-life Number of half-lives
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 3 Write the half-life equality and conversion factors. STEP 4 Set up the problem to calculate the needed quantity. 1 half-life 2 half-lives 64 mg 32 mg 16 mg I-123 Answer is B.