1. Half-Life Practice Problems

2. Question 1
The half-life of 222Rn is 4 days. After how many days is the amount remaining ¼ of the original amount?

3. Answer
After 4 days ½ remains, after 8 days ½ of ½ (1/4) remains
Answer: 8 Days

4. Question 2
The half-life of a material is 100 years. If you have 1,000 g, how much will remain after 500 years?

5. Answer After 100 years ½ remains After 200 years ¼ remains (1/2 of ½)
1/32 of g = 31.25g or (1000/32=31.25g)

6. Question 3
Barium-122 has a half-life of 2 minutes. A fresh sample weighing 80g was obtained. If it takes 10 minutes to set up an experiment using barium-122, how much barium-122 will be left when the experiment begins?

7. Answer
Every half-life, 2 minutes, half of the original amount will undergo nuclear decay.
Time
Mass
Start
80g
2 min
40g
4 min
20g
6 min
10g
8 min 5g
10 min
2.5g

8. Question 4
If 10 mg of iodine-131 is given to a patient, how much is left after 24 days? The half-life of iodine-131 is 8 days.

9. Answer
Since the half-life is 8 days, 24 days corresponds to 3 half-lives. After one half- life 5 mg are left; after two half-lives, 2.5 mg; and after 3 half-lives 1.25 mg remain.

10. Question 5
Iodine-131 is used to destroy thyroid tissue in the treatment of an overactive thyroid. The half-life of iodine-131 is 8 days. If a hospital receives a shipment of 200 g of iodine-131, how much I-131 would remain after 32 days?

11. Answer
32 days/8days => 4 half-lives
½ x ½ = ¼ X ½ = 1/8 X ½ =1/16
200g/16 = 12.5g remain after 32 days

12. Question 6
An isotope of cesium (cesium-137) has a half-life of 30 years. If 1.0 mg of cesium-137 disintegrates over a period of 90 years, how many mg of cesium-137 would remain?

13. Answer
90 years/30 years = 3 half-lives
½ X ½ = ¼ X ½ = 1/8 remains of cesium-137
1.0 mg/8 = 0.125g remains of cesium-137

14. Question 7
Technetium-99 is used for brain scans. If a laboratory receives a shipment of 200g of this isotope and after 24 hours only 12.5g of this isotope remain, what is the half-life of technetium-99?

15. Answer
200/2 =100
100/2=50
50/2=25
25/2=12.5g => 4 half-lives
24hr/4= 6 hours