Standard chemistry worksheet designed to help students practice calculating radioactive half-lives using various isotopes and time periods.

Let’s solve each half-life problem step by step. Half-life is the time required for half of a radioactive substance to decay. After each half-life, the amount remaining is halved.

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Problem 1:

> 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?

Solution:

- Half-life = 30 years
- Total time = 90 years
- Number of half-lives = 90 / 30 = 3

Starting amount = 1.0 mg

After 1st half-life (30 yrs): 1.0 → 0.5 mg
After 2nd half-life (60 yrs): 0.5 → 0.25 mg
After 3rd half-life (90 yrs): 0.25 → 0.125 mg

✔ Answer: 0.125 mg

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Problem 2:

> Actinium-226 has a half-life of 29 hours. If 100 mg of actinium-226 disintegrates over a period of 58 hours, how many mg of actinium-226 will remain?

Solution:

- Half-life = 29 hours
- Total time = 58 hours
- Number of half-lives = 58 / 29 = 2

Starting amount = 100 mg

After 1st half-life (29 hrs): 100 → 50 mg
After 2nd half-life (58 hrs): 50 → 25 mg

✔ Answer: 25 mg

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Problem 4:

> The half-life of isotope X is 2.0 years. How many years would it take for a 4.0 mg sample of X to decay and have only 0.50 mg of it remain?

Solution:

We need to find how many half-lives it takes to go from 4.0 mg → 0.50 mg.

Let’s track the decay:

Start: 4.0 mg
After 1 half-life (2 yrs): 4.0 → 2.0 mg
After 2 half-lives (4 yrs): 2.0 → 1.0 mg
After 3 half-lives (6 yrs): 1.0 → 0.5 mg

So, it takes 3 half-lives → 3 × 2.0 years = 6.0 years

✔ Answer: 6.0 years

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Problem 5:

> Selenium-83 has a half-life of 25.0 minutes. How many minutes would it take for a 10.0 mg sample to decay and have only 1.25 mg of it remain?

Solution:

Start: 10.0 mg
Target: 1.25 mg

Track decay:

After 1 half-life (25 min): 10.0 → 5.0 mg
After 2 half-lives (50 min): 5.0 → 2.5 mg
After 3 half-lives (75 min): 2.5 → 1.25 mg

✔ Answer: 75.0 minutes

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Problem 6:

> The half-life of Po-218 is three minutes. How much of a 2.0 gram sample remains after 15 minutes?

Solution:

- Half-life = 3 minutes
- Total time = 15 minutes
- Number of half-lives = 15 / 3 = 5

Starting amount = 2.0 grams

After each half-life, divide by 2:

After 1: 2.0 → 1.0 g
After 2: 1.0 → 0.5 g
After 3: 0.5 → 0.25 g
After 4: 0.25 → 0.125 g
After 5: 0.125 → 0.0625 g

✔ Answer: 0.0625 grams

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## ✔ Final Answers Summary:

1. 0.125 mg
2. 25 mg
4. 6.0 years
5. 75.0 minutes
6. 0.0625 grams

Let me know if you’d like to see the exponential decay formula version too!