Educational worksheet on half-life calculations in radioactive decay.

Let’s go step by step through each question using the half-life concept.

We’re told:
- The isotope starts with 120 grams.
- Its half-life is 5 years → meaning every 5 years, the amount halves.

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Question 1: How much of the isotope (in grams) will remain after 5 years?

→ 5 years = 1 half-life
→ So we halve the starting amount once:
120 g × ½ = 60 grams

✔ Correct as shown.

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Question 2: How much... after 10 years?

→ 10 years ÷ 5 years per half-life = 2 half-lives
→ Halve twice:
First: 120 × ½ = 60
Second: 60 × ½ = 30
Or: 120 × (½)² = 120 × ¼ = 30 grams

✔ Correct.

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Question 3: How much... after 15 years?

→ 15 5 = 3 half-lives
→ 120 × (½)³ = 120 × ⅛ = 15 grams

✔ Correct.

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Question 4: How many half lives would occur in 30 years?

→ 30 ÷ 5 = 6 half-lives

Then: How much remains?

→ 120 × (½)^6 = 120 × (1/64) = 120 ÷ 64

Let’s calculate that:

120 ÷ 64 = ?

Divide numerator and denominator by 8:
15 ÷ 8 = 1.875 grams

✔ Correct as shown.

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Question 5: How long would it take for the mass to be reduced to 7.5 grams?

Start at 120 g.

After 1 half-life (5 yrs): 60 g
After 2: 30 g
After 3: 15 g
After 4: 7.5 g ← this is what we want!

So it takes 4 half-lives.

Each half-life is 5 years → 4 × 5 = 20 years

✔ Correct.

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Question 6: How long to reduce to 3.75 grams?

Continue from above:

After 4 half-lives: 7.5 g
After 5 half-lives: 7.5 × ½ = 3.75 g

So it takes 5 half-lives → 5 × 5 = 25 years

✔ Correct.

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All answers in the worksheet are correct. But since you asked me to solve the problem accurately — and all problems are already solved correctly in the image — I’ll confirm each final answer below.

Final Answer:
1) 60 grams
2) 30 grams
3) 15 grams
4) 6 half-lives; 1.875 grams
5) 20 years
6) 25 years