1. Half-Life Notes

2. Half-Life: the amount of time it takes half of a radioactive sample to decay.
Total
Time
Half-Life #
Fraction of Radioactive Atoms Remaining
Fraction of Radioactive Atoms Decayed 1 2 3 4 5 6 1
1/8
7/8
1/16
15/16
1/32
31/32
1/64
63/64

3. Example 1) Assuming a half-life of 1599 years, how many years will be needed for the decay of 15/16 of a given amount of radium-226?
Total
Time
Half-Life #
Fraction of Radioactive Atoms Remaining
Fraction of Radioactive Atoms Decayed 1 2 3 4
Need 4 half-lives
4 * 1599 years = 6396 years
0 yrs 1
1599 yrs
3198 yrs
1/8
4797 yrs
7/8
1/16
6396 yrs
15/16

4. Example 2) The half-life of radon-222 is 3. 824 days
Example 2) The half-life of radon-222 is days. How much time must past for ¼ of a given amount of radon to remain?
Total
Time
Half-Life #
Fraction of Radioactive Atoms Remaining
Fraction of Radioactive Atoms Decayed 1 2
Need 2 half-lives
2 * days= days
0 days 1
3.824 days
7.648 days

5. Example 3) The half-life of polonium-218 is 3. 0min
Example 3) The half-life of polonium-218 is 3.0min. If you start with 16mg of polonium-218, how much time must pass for only 1.0mg to remain?
Starting Amount = 16 mg
Remaining Amount = 1.0 mg
Fraction Remainig = 1.0 / 16 mg
= 1/16
Total
Time
Half-Life #
Fraction of Radioactive Atoms Remaining
Fraction of Radioactive Atoms Decayed 1 2 3 4
0 min 1
Need 4 half-lives
4* 3.0min = 12 min
3.0 min
6.0 min
1/8
9.0 min
7/8
1/16
12 min
15/16

6. After 4797 years, how much of an original 0
After 4797 years, how much of an original 0.250g sample of radium-226 remains? Its half-life is 1599 years.

7. The half-life of radium-224 is 3. 66 days
The half-life of radium-224 is 3.66 days. What was the original mass of radium-224 if g remains after 7.32 days?