1. Half Life Practice

2. If the half-life of iodine-131 is 8
If the half-life of iodine-131 is 8.10 days, how long will it take a g sample to decay to 6.25 g?

3. What percentage of 50g is 6.25g?
6.25g ÷ 50g = 12.5%
How many half-lives leave you with 12.5% of the parent isotope? 3
If 1 half-life = 8.1 days, 3 half-lives are equal to 24.3 days.
8.1 days × 3 = 24.3 days

4. The half-life of hafnium-156 is 0. 025 seconds
The half-life of hafnium-156 is seconds. How long will it take a 560 g sample to decay to one-fourth       of its original mass?

5. One-fourth is equal to 25%.
How many half-lives result in 25% of the parent isotope being left? 2
0.025 seconds/half-life × 2 half-lives= 0.05 sec

6. Chromium-48 has a short half-life of 21. 6 hours
Chromium-48 has a short half-life of 21.6 hours. How long will it take g of chromium-48 to decay       to g?

7. What percentage of 360g is 11. 25g. 11. 25g ÷ 360g × 100% = 3
What percentage of 360g is 11.25g? 11.25g ÷ 360g × 100% = 3.125% How many half-lives result in 3.125% of the parent isotope? 5 If 1 half life = 21.6 hours, then 5 half-lives would be equal to: 21.6hrs × 5 = 108 hrs

8. Potassium-42 has a half-life of 12. 4 hours
Potassium-42 has a half-life of 12.4 hours. How much of an 848 g sample of potassium-42 will be left after       62.0 hours?

9. *T-chart time! OR… 62 hours ÷ 12.4 hours/HL = 5 Half-Lives
Half Life
Amount (g)
0 (initial)
848
1 (12.4 hours)
424
2 (24.8 hours)
212
3 (37.2 hours)
106
4 (49.6 hours) 53
5 (62.0 hours)
26.5
OR… 62 hours ÷ 12.4 hours/HL = 5 Half-Lives
5 half lives leave you with 3.125% of your parent isotope, so 848g × 3.125% = 26.5g

10. Carbon-14 has a half-life of 5730 years
Carbon-14 has a half-life of 5730 years. How much of a 144 g sample of carbon-14 will remain after       1.719 × 104 years?

11. 1.719 × 104 = 17,190 years If 1 half-life is equal to 5730 years, how many half-lives are in 17,190 years? 17,190years ÷ 5730years/HL = 3 HL *T-chart time!
Half Life
Amount (g)
144 1 72 2 36 3 18

12. What is the half-life of a 100
What is the half-life of a g sample of nitrogen-16 that decays to 12.5 grams in 21.6 seconds?

13. First, we realize that we are left with 12
First, we realize that we are left with 12.5% of the parent isotope (Nitrogen-18).
We need to find out how many half-lives leave us with 12.5% of the parent isotope.
1 half life= 50% parent isotope
2 half lives= 25% parent isotope (half of 50%)
3 half lives= 12.5% parent isotope (half of 25%)
If 21.6 seconds is enough time for 3 half-lives,
1 half life = 7.2 seconds. (21.6 divided by 3)

14. All isotopes of technetium are radioactive, but they have widely varying half-lives. If an gram sample of technetium-99 decays to g of technetium-99 in 639,000 years, what is its half-life?

15. We are left with 100g out of 800g. What percentage is that?
12.5%
How many half-lives leave us with 12.5% of the parent isotope? 3
If 3 half-lives are equal to 639,000 years, how long is 1 half-life?
213,000

16. A 208 g sample of sodium-24 decays to 13. 0 g of sodium-24 within 60
A 208 g sample of sodium-24 decays to 13.0 g of sodium-24 within 60.0 hours. What is the half-life of this       radioactive isotope?

17. We are left with 13g out of 208g. What percentage is that?
13g ÷ 208g × 100% = 6.25%
How many half-lives result in 6.25% of the parent isotope? 4
If 4 half-lives have occurred in 60 hours, how much time is in 1 half-life?
60 hours ÷ 4 half-lives = 15 hours per half-life