Nuclear Chemistry Half-Life Practice Worksheet

Let's solve each question step by step using the concept of half-life in nuclear chemistry.

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1. Sodium-24 has a half-life of 15 hours.

#### a) Fill in the chart for how much sodium-24 remains at each interval.

We start with 64 grams, and every 15 hours, the mass is halved.

| Time (hrs) | 0 | 15 | 30 | 45 | 60 | 75 | 90 | 105 |
|------------|-----|-----|-----|-----|-----|-----|-----|-----|
| Mass (g) | 64 | 32 | 16 | 8 | 4 | 2 | 1 | 0.5 |

> Each 15-hour interval = one half-life.

#### b) What percentage of the sample will remain at 45 hours?

At 45 hours:
- 45 ÷ 15 = 3 half-lives
- After 3 half-lives: $ \frac{1}{2^3} = \frac{1}{8} = 12.5\% $

✔ Answer: 12.5%

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2. Lawrencium-247 has a half-life of 8 seconds.

Start with 96 mg, want to find when only 3 mg remains.

We need to determine how many half-lives it takes to go from 96 mg → 3 mg.

Let’s divide:

- 96 → 48 (1st half-life)
- 48 → 24 (2nd)
- 24 → 12 (3rd)
- 12 → 6 (4th)
- 6 → 3 (5th)

So, 5 half-lives needed.

Each half-life = 8 seconds → $ 5 × 8 = 40 $ seconds

✔ Answer: 40 seconds

Now fill the table:

| Time (s) | 0 | 8 | 16 | 24 | 32 | 40 | 48 | 56 |
|----------|----|----|----|----|----|----|----|----|
| Mass (mg)| 96 | 48 | 24 | 12 | 6 | 3 | 1.5| 0.75 |

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3. Fermium-253 decays to 6.25% of its original amount in 18 days.

We are told that after 18 days, only 6.25% remains.

Let’s find how many half-lives this corresponds to:

- 6.25% = $ \frac{6.25}{100} = 0.0625 $
- $ 0.0625 = \frac{1}{16} = \frac{1}{2^4} $

So, 4 half-lives occur in 18 days.

Therefore, half-life = $ \frac{18}{4} = 4.5 $ days

✔ Answer: 4.5 days

Now fill the table:

| Time (days) | 0 | 4.5 | 9 | 13.5 | 18 | 22.5 | 27 | 31.5 |
|-------------|------|------|------|------|------|------|------|------|
| Mass (%) | 100% | 50% | 25% | 12.5%| 6.25%| 3.125%| 1.5625%| 0.78125% |

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4. Zinc-71 has a half-life of 2.4 minutes.

Start with 18 g, find how much remains after 7.2 minutes.

Number of half-lives: $ \frac{7.2}{2.4} = 3 $

After 3 half-lives: $ \frac{1}{2^3} = \frac{1}{8} $ remains

$ 18 × \frac{1}{8} = 2.25 $ grams

✔ Answer: 2.25 grams

Fill the table:

| Time (min) | 0 | 2.4 | 4.8 | 7.2 | 9.6 | 12.0 | 14.4 | 16.8 |
|------------|-----|-----|-----|-----|-----|------|------|------|
| Mass (g) | 18 | 9 | 4.5 | 2.25| 1.125| 0.5625| 0.28125| 0.140625 |

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5. Need 3 grams of sodium-24 for experiment. Amazon delivers in 90 hours. What minimum must be shipped?

Sodium-24 has a half-life of 15 hours.

We need 3 grams after 90 hours.

Work backwards — how much was there initially?

Number of half-lives in 90 hours: $ \frac{90}{15} = 6 $

After 6 half-lives, the remaining amount is $ \frac{1}{2^6} = \frac{1}{64} $ of original.

So:
$$
\text{Original mass} = 3 × 64 = 192 \text{ grams}
$$

✔ Answer: 192 grams

Fill the table (working backward):

| Time (hrs) | 0 | 15 | 30 | 45 | 60 | 75 | 90 |
|------------|-----|-----|-----|-----|-----|-----|-----|
| Mass (g) | 192 | 96 | 48 | 24 | 12 | 6 | 3 |

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6. Radon-222 has a half-life of 3.82 days. How long before 1/16th remains?

We want $ \frac{1}{16} $ of original sample.

Note: $ \frac{1}{16} = \frac{1}{2^4} $ → 4 half-lives

Time = $ 4 × 3.82 = 15.28 $ days

✔ Answer: 15.28 days

Fill the table:

| Time (days) | 0 | 3.82 | 7.64 | 11.46 | 15.28 |
|-------------|-------|-------|-------|-------|-------|
| Mass | 100% | 50% | 25% | 12.5% | 6.25% |

(Or as fractions: 1, ½, ¼, ⅛, ¹⁄₁₆)

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✔ Final Answers Summary:

1. a) Chart filled: 64, 32, 16, 8, 4, 2, 1, 0.5
b) 12.5%

2. a) 40 seconds
Table: 96, 48, 24, 12, 6, 3, 1.5, 0.75

3. a) 4.5 days
Table: 100%, 50%, 25%, 12.5%, 6.25%, ...

4. a) 2.25 grams
Table: 18, 9, 4.5, 2.25, ...

5. 192 grams
Table: 192, 96, 48, 24, 12, 6, 3

6. 15.28 days
Table: 100%, 50%, 25%, 12.5%, 6.25%

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