Radioactivity: background theory worksheet with fill-in-the-blank, matching, table completion, and calculation questions.

Let's go through each question in the worksheet and solve them step by step.

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1. Fill in the blanks using correct terms

Original text:
> Our understanding of atomic structure has improved over time. Thousands of years ago, atoms were imagined as the ________ possible lumps of matter that were the same all the way through. In 1897, Thomson suggested a model known as the plum pudding (chocolate chip cookie) model, in which ________ charged particles were embedded in a ________ charged material. This model was refined in 1911 by a team that was led by Rutherford, who suggested atoms contained mostly ________ with a central ________ nucleus surrounded by electrons. In the model that we use today, the electrons are arranged in ________ and small amounts of ________ are absorbed or released when electrons move between energy levels in these shells.

Correct answers:

- indivisible
- negatively
- positively
- empty space
- dense, positively charged
- energy levels (or electron shells)
- energy

✔ Completed sentence:

> Our understanding of atomic structure has improved over time. Thousands of years ago, atoms were imagined as the indivisible possible lumps of matter that were the same all the way through. In 1897, Thomson suggested a model known as the plum pudding (chocolate chip cookie) model, in which negatively charged particles were embedded in a positively charged material. This model was refined in 1911 by a team that was led by Rutherford, who suggested atoms contained mostly empty space with a central dense, positively charged nucleus surrounded by electrons. In the model that we use today, the electrons are arranged in energy levels and small amounts of energy are absorbed or released when electrons move between energy levels in these shells.

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2. Match sub-atomic particles to their mass and charge

We have three columns:

| Mass (amu) | Sub-atomic particle | Charge |
|--------------|---------------------|--------|
| 1 | Electron | -1 |
| 1 | Neutron | 0 |
| nearly zero | Proton | +1 |

✘ Wait — this is incorrect! Let's fix it.

Actually:
- Electron: mass = nearly zero (≈ 0.0005 amu), charge = -1
- Neutron: mass = 1 amu, charge = 0
- Proton: mass = 1 amu, charge = +1

✔ Correct connections:

| Mass (amu) | Sub-atomic particle | Charge |
|--------------|---------------------|--------|
| nearly zero → Electron | -1 |
| 1 → Neutron | 0 |
| 1 → Proton | +1 |

So draw lines like:
- Electron → nearly zero (mass), -1 (charge)
- Neutron → 1 (mass), 0 (charge)
- Proton → 1 (mass), +1 (charge)

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3. Complete the table for isotopes

We need:
- Number of protons = atomic number (Z)
- Number of neutrons = mass number (A) − atomic number (Z)

| Isotope | $^{241}_{95}\text{Am}$ | $^{238}_{92}\text{U}$ | $^{226}_{88}\text{Ra}$ | $^{14}_{6}\text{C}$ | $^{222}_{86}\text{Rn}$ | $^{133}_{54}\text{Xe}$ |
|---------------|--------------------------|-------------------------|--------------------------|----------------------|--------------------------|---------------------------|
| Number of protons | 95 | 92 | 88 | 6 | 86 | 54 |
| Number of neutrons | 241 − 95 = 146 | 238 − 92 = 146 | 226 − 88 = 138 | 14 − 6 = 8 | 222 − 86 = 136 | 133 − 54 = 79 |

✔ Final Table:

| Isotope | $^{241}_{95}\text{Am}$ | $^{238}_{92}\text{U}$ | $^{226}_{88}\text{Ra}$ | $^{14}_{6}\text{C}$ | $^{222}_{86}\text{Rn}$ | $^{133}_{54}\text{Xe}$ |
|---------------|--------------------------|-------------------------|--------------------------|----------------------|--------------------------|---------------------------|
| Protons | 95 | 92 | 88 | 6 | 86 | 54 |
| Neutrons | 146 | 146 | 138 | 8 | 136 | 79 |

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4. Three precautions for handling radioactive sources safely

✔ Answers (any three):

1. Always wear appropriate protective clothing, such as lab coats, gloves, and safety goggles.
2. Minimize exposure time – handle sources quickly and efficiently.
3. Use shielding – keep radioactive materials behind lead or concrete barriers when not in use.
4. Maintain distance – stay as far away from the source as possible.
5. Never eat, drink, or smoke in the lab where radioactive materials are handled.
6. Label all containers clearly and store them properly.

Choose any three. Example:

- Wear protective gear (gloves, lab coat).
- Use tongs or remote tools to handle sources.
- Store sources in lead-lined containers.

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5. Radioactive decay of Fermium-252

#### (a) Half-life calculation

Given:
- Initial mass = 100 g
- Half-life = 25 hours
- Time elapsed = 100 hours

Number of half-lives = $ \frac{100}{25} = 4 $

After each half-life, mass halves:

- After 1st: 50 g
- After 2nd: 25 g
- After 3rd: 12.5 g
- After 4th: 6.25 g

✔ So, mass remaining = 6.25 g

Answer: mass = 6.25 g

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#### (b) Alpha decay of $^{252}_{100}\text{Fm}$

Alpha decay emits an alpha particle: $^4_2\text{He}$

So:

$$
^{252}_{100}\text{Fm} \rightarrow ^{A}_{Z}\text{Cf} + ^4_2\text{He}
$$

Conservation of mass and charge:

- Mass: $ 252 = A + 4 $ → $ A = 248 $
- Atomic number: $ 100 = Z + 2 $ → $ Z = 98 $

Californium (Cf) has atomic number 98, so the product is:

$$
^{248}_{98}\text{Cf}
$$

✔ Answer:
- Atomic mass: 248
- Atomic number: 98

So fill in:
```
[248] Cf
[98]
```

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✔ Final Answers Summary

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1. Fill in the blanks:
- indivisible
- negatively
- positively
- empty space
- dense, positively charged
- energy levels
- energy

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2. Matching:
- Electron → nearly zero mass, -1 charge
- Neutron → 1 amu, 0 charge
- Proton → 1 amu, +1 charge

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3. Table:

| Isotope | Am | U | Ra | C | Rn | Xe |
|---------------|----|----|----|----|----|----|
| Protons | 95 | 92 | 88 | 6 | 86 | 54 |
| Neutrons | 146| 146| 138| 8 | 136| 79 |

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4. Precautions (example):
1. Wear protective clothing.
2. Minimize exposure time.
3. Use shielding and maintain distance.

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5. (a) Mass remaining after 100 hours: 6.25 g
(b) Product: $^{248}_{98}\text{Cf}$ → Fill in:
- 248 Cf
- 98

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