1. Chapter 9 Nuclear Radiation
9.4
Half-Life of a Radioisotope

2. 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.
The decay curve for I-131 shows that one-half the sample
decays every 8 days.

3. Half-Lives of Some Radioisotopes

4. Guide to Using Half-Lives

5. 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.
Given: 36 mg, years, half-life of 38.1 years
Needed: mg Sr-90 remaining
Step 2 Write a plan to calculate unknown quantity.
Half-life
152.4 years number of half-lives
Number of half-lives
36 mg Sr mg Sr-90 remaining

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 3 Write the half-life equality and conversion factors.
1 half-life = 38.1 years
38.1 years and half-life
1 half-life years

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 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 half-lives 3 half-lives 4 half-lives
36 mg  18 mg  9 mg  mg  2.3 mg Sr-90

8. 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?

9. Solution
Carbon-14 was used to determine the age of the Dead Sea Scrolls. If the Dead Sea Scrolls were determined to be 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 = half-life
5730 years

10. 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

11. 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.
Given: 64 mg, 26 hours, half-life of 13 hours
Needed: mg I-123 remaining
Step 2 Write a plan to calculate unknown quantity.
Half-life
26 hours number of half-lives
Number of half-lives
64 mg I mg I-123 remaining

12. 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.
1 half-life = 13 hours
13 hours and half-life
1 half-life hours

13. 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 4 Set 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 half-lives
64 mg  32 mg  16 mg I-123
The answer is B, 16 mg of I-123 remain.