1. 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.

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.

3. 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

4. Half-Lives of Some Radioisotopes

5. Guide to Using Half-Lives

6. 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 1 State the given and needed quantities.
ANALYZE Given Need
THE PROBLEM mg yrs milligrams Sr-90
Sr-90 half-life = 38.1 yrs

7. 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 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

8. 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.

9. 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 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

10. 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?

11. 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 yrs old fraction of
C-14 half-life = 5730 yrs half-life passed

12. 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

13. 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.

14. 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

15. 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 mg I-123 mg of I-123
I-123 half-life = 13 hours remaining
Half-life
Number of half-lives

16. 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 Answer is B.