This answer key provides the correct solutions and step-by-step calculations for a radioactivity and half-life review worksheet.

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## 🧪 Question 1:
What is the difference between radioactivity and nuclear radiation?

✔ Answer:
> *Radioactivity is the process of nuclear decay (an unstable isotope emitting energy/a particle to become more stable). Nuclear radiation is that energy or particle being emitted.*

🔹 Explanation:
- Radioactivity refers to the *process* — the spontaneous disintegration of unstable atomic nuclei.
- Nuclear radiation refers to the *products* of that process — alpha particles, beta particles, gamma rays, etc.
Think of it like this:
> Radioactivity = the *event* (like a volcano erupting)
> Nuclear radiation = the *stuff* that comes out (lava, ash, gas)

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## 🛡️ Question 2:
Which type of radiation can be blocked by…

a. A piece of paper? → Alpha
b. A piece of wood? → Beta
c. A large block of concrete? → Gamma

✔ Extension Opportunity Answer:
> *Alpha particles are the largest, so they move the slowest and cannot penetrate objects easily. Gamma particles are the smallest and have no charge, so they penetrate more easily.*

🔹 Explanation:
Radiation types differ in mass, charge, and penetration power:

| Type | Composition | Charge | Penetration Power | Blocked By |
|-----------|-------------------|--------|--------------------------|-------------------------|
| Alpha | Helium nucleus (2p+2n) | +2 | Very low | Paper, skin |
| Beta | High-speed electron | -1 | Moderate | Wood, aluminum foil |
| Gamma | High-energy photon | 0 | Very high | Lead, thick concrete |

Alpha particles are heavy and charged → easily stopped.
Gamma rays are massless and uncharged → very penetrating.

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## ⏳ Question 3:
What is a half-life?

✔ Answer:
> *The time it takes for half of the material you started with to decay.*

🔹 Explanation:
Half-life is a constant for each radioactive isotope. It doesn’t matter if you start with 1 gram or 1000 grams — after one half-life, half remains. After two half-lives, a quarter remains, and so on.

Example: If half-life = 5 years, then:
- Start: 100g
- After 5 yrs: 50g
- After 10 yrs: 25g
- After 15 yrs: 12.5g

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## 🔢 Question 4:
If we start with 400 atoms... how many remain after…

- 1 half-life → 200
- 2 half-lives → 100
- 3 half-lives → 50
- 4 half-lives → 25

🔹 Explanation:
Each half-life cuts the amount in half:
- 400 → 200 → 100 → 50 → 25

This is exponential decay:
> Remaining = Initial × (1/2)^n, where n = number of half-lives.

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## 🔢 Question 5:
Start with 16 grams → how much after 3 half-lives?

✔ Answer: 2 grams

🔹 Explanation:
16 → 8 → 4 → 2
After each half-life, divide by 2.
Or use formula:
> 16 × (1/2)^3 = 16 × 1/8 = 2 grams

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## 📊 Question 6:
Carbon-14 sample decaying for 22,920 years → now 35.0 g. What was original size? (Half-life = 5,730 years)

✔ Answer: 560 grams

🔹 Explanation:
Step 1: Find number of half-lives passed:
> 22,920 ÷ 5,730 = 4 half-lives

Step 2: Work backwards — each half-life doubles the amount going back in time:
> Current = 35g
> Before 1st half-life: 35 × 2 = 70g
> Before 2nd: 70 × 2 = 140g
> Before 3rd: 140 × 2 = 280g
> Before 4th: 280 × 2 = 560g

Alternatively:
> Original = Current × 2^n = 35 × 2^4 = 35 × 16 = 560 grams

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## 💀 Question 7:
Skeleton sample has 3.125% carbon-14 left. How old? (Assume started at 100%)

✔ Answer: 28,650 years

🔹 Explanation:
We know half-life of C-14 = 5,730 years.

Find how many half-lives correspond to 3.125% remaining:

Start: 100%
→ 1 half-life: 50%
→ 2: 25%
→ 3: 12.5%
→ 4: 6.25%
→ 5: 3.125% ← matches!

So, 5 half-lives have passed.

Age = 5 × 5,730 = 28,650 years

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## 📉 Question 8:
Started with 120g → now 15g. How many half-lives?

✔ Answer: 3 half-lives

🔹 Explanation:
120 → 60 → 30 → 15
That’s 3 steps → 3 half-lives

Check: 120 × (1/2)^3 = 120 × 1/8 = 15 ✔️

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## ⏱️ Question 9:
Isotope X has half-life = 2.0 years. How long for 4.0 mg to decay to 0.50 mg?

✔ Answer: 6.0 years

🔹 Explanation:
4.0 → 2.0 → 1.0 → 0.50
That’s 3 half-lives.

Each half-life = 2 years → 3 × 2 = 6.0 years

Formula check:
> 4.0 × (1/2)^n = 0.50
> (1/2)^n = 0.50 / 4.0 = 0.125
> (1/2)^n = 1/8 → n = 3

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## ✔ Final Summary:

All problems revolve around understanding:
- The nature of different types of radiation (alpha, beta, gamma)
- The concept of half-life as a fixed time period for decay
- Exponential decay: halving the amount per half-life
- Working forward (decay) or backward (finding original amount)
- Applying math: multiplying/dividing by 2, or using powers of 1/2

This worksheet is excellent for reinforcing foundational nuclear chemistry concepts — especially useful for middle/high school or intro college courses.

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