THE ATOM Lesson 4 Check for Understanding
Half-Life Calculations (SHOW ALL WORK!!)
- Suppose we have 100 nuclei of a radioactive isotope. After one half-life, half of the nuclei will have disintegrated,
leaving 50 nuclei.
a. How many nuclei will be left after the second half-life? 100 - > 50 - > 25
b. How many nuclei would you predict would remain after the third half-life? 100 - > 50 - > 25 - > 12.5
- Element X has a mass of 300g and a ½ life of 10 years. How many grams will remain after 40 years?
Hint: first determine how many ½ lives in 40 years.
40 / 10 = 4
300 - > 150 - > 75.0 - > 37.5
- Element Z has a mass of 430g. Scientists determined it to have a ½ life of 5 years. How many grams of element Z will
remain after 15 years? Show your work. Hint: first determine how many ½ lives
15/5=3
430 - > 215 - > 107.5 - > 53.75
- Phosphorus-32 is a radioisotope with a half-life of 14.3 days. If you start with 4.0 g of phosphorus-32, how many
grams will remain after 57.2 days? How many half-lives will have passed? Hint: first determine how many ½ lives 57.2 / 14.3 = 4 4.0 - > 2.0 - > 1.0 - > 0.5 - > 0.25
- Sodium-24 has a half-life of 15 hours. How much sodium-24 will remain in an 18.0-g sample after 60 hours?
Hint: first determine how many ½ lives
60 / 15 = 4
18.0 - > 9.0 → 4.5 - > 2.25 - > 1.125
- After 42 days, a 2.0-g sample of phosphorus-32 contains only 0.25 g of isotope. What is the half-life of phosphorus-32? Hint: first determine how many ½ lives
2.0 - > 1.0 - > 0.5 - > 0.25
3
42 / 3 = 14
- 8.0g of phosphorus-32 takes 6 weeks (42 days) to arrive from the lab in Europe. Its half life is 14 days. What is the
amount remaining? Hint: first determine how many ½ lives
42 / 14 = 3
8.0 - > 4.0 → 2.0 - > 1.0
- Iodine-131 has a half life of 8 days. What fraction of the original sample would remain at the end of 32 days?
Hint: first determine how many ½ lives
32 / 8 = 4
1 - > .5 - > .25 - > .125 - > .0625
1/16
- The half-life of chromium-51 is 28 days. If the sample contained 510 grams, how much Cr-51 would remain after 56
days? Hint: first determine how many ½ lives
56/28 = 2
510 - > 255 - > 127.5
- If 20.0 g of a radioactive isotope are present at 1:00 PM and 5.0 g remain at 2:00 PM, what is the half life of the
isotope? Hint: first determine how many ½ lives
5 - > 10 - > 20
1 hour / 2 = 30 minutes
- The half life of iodine-125 is 60 days. What fraction of iodine-125 nuclides would be left after 360 days?
Hint: first determine how many ½ lives
360 / 60 = 6
1 - > 1/2 - > 1/4 - > 1/8 - > 1/16 - > 1/32 - > 1/64
1/64 of the nuclides would be left
- Titanium-51 decays with a half life of 6 minutes. What fraction of titanium would remain after one hour?
Hint: first determine how many ½ lives
60 / 6 = 10
1 - > 1/2 - > 1/4 - > 1/8 - > 1/16 - > 1/32 - > 1/64
- A medical institution requests 1.0 g of bismuth-214, which has a half life of 20 min. How many grams of
bismuth-214 must be prepared if the shipping time is 2.0 hrs? Hint: first determine how many ½ lives
120 / 20 = 6
1.0 * 2 * 2 * 2 * 2 * 2 * 2
64
64 - > 32 - > 16 → 8 - > 4 - > 2 - > 1
- Strontium-85 has a half life of 65.2 days. How long will it take for 20.0 g to decay to 5.0 g?
Hint: first determine how many ½ lives
20 - > 10 → 5
65.2 * 2 = 130.4
Answers: 1) a. 25 nuclei b. 12.5 nuclei 2) 18.75g 3) 53.75g 4) 0.25g 5) 1.125g
6) 14 days 7) 1.0 g 8) 1/16 9) 127.5g 10) 30. min 11) 1/64 12) 1/1024
13) 64g 14) 130.4 days