Nuclear physics

1. What did Rutherford scattering demonstrate?

1. Electrons orbit in shells
2. The atom has a tiny, dense, positive nucleus with mostly empty space
3. Neutrons exist
4. Atoms are indivisible

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B: The atom has a tiny, dense, positive nucleus with mostly empty space. A few alpha particles were deflected through large angles.

2. Which equation links half-life and decay constant?

1. T½ = λ ÷ ln2
2. T½ = ln2 ÷ λ
3. T½ = λ²
4. T½ = 1 ÷ λ²

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B: T½ = ln2 ÷ λ. A larger decay constant means a shorter half-life.

3. What is activity?

1. The number of undecayed nuclei
2. The rate of decay, A = λN
3. The energy of emitted radiation
4. The mass of the sample

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B: The rate of decay, A = λN. Activity is measured in becquerels.

4. What is conserved in a nuclear equation?

1. Only mass
2. Nucleon number and proton number
3. Only charge of electrons
4. Nothing

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B: Nucleon number and proton number. Both must balance on each side of the equation.

5. What does 'random' decay mean?

1. Decay never happens
2. Each nucleus has a constant probability of decaying per unit time, but which decays cannot be predicted
3. All nuclei decay at once
4. Decay depends on temperature

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B: Each nucleus has a constant probability of decaying per unit time, but which decays cannot be predicted. Only average behaviour across many nuclei is predictable.

6. A radioactive sample's activity falls from 800 Bq to 100 Bq. How many half-lives have passed?

1. 2
2. 3
3. 4
4. 8

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B: 3. 800 → 400 → 200 → 100 is three halvings.

7. A nuclide has a half-life of 6.0 hours. What is its decay constant?

1. 3.2 × 10⁻⁵ s⁻¹
2. 1.9 × 10⁻⁴ s⁻¹
3. 4.6 × 10⁻⁵ s⁻¹
4. 0.12 s⁻¹

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A: 3.2 × 10⁻⁵ s⁻¹. λ = ln2 ÷ T½ = 0.693 ÷ (6.0 × 3600 s) = 3.2 × 10⁻⁵ s⁻¹. Forgetting ln2 gives 4.6 × 10⁻⁵; using 1 hour = 3600 s but T½ = 1 h gives 1.9 × 10⁻⁴.

8. A sample contains 2.0 × 10⁶ undecayed nuclei and has λ = 3.0 × 10⁻³ s⁻¹. What is its activity?

1. 1.5 × 10⁻⁹ Bq
2. 6.7 × 10⁸ Bq
3. 6.0 × 10³ Bq
4. 2.0 × 10⁶ Bq

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C: 6.0 × 10³ Bq. A = λN = 3.0 × 10⁻³ × 2.0 × 10⁶ = 6.0 × 10³ Bq. Dividing N by λ, or λ by N, are common slips.

9. Which change takes place inside the nucleus during β⁻ decay?

1. A proton and electron combine to form a neutron
2. A neutron changes into a proton and a positron
3. A proton changes into a neutron, positron and neutrino
4. A neutron changes into a proton, electron and antineutrino

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D: A neutron changes into a proton, electron and antineutrino. β⁻ decay converts a neutron to a proton, emitting an electron and an antineutrino. The proton number rises by 1; the nucleon number is unchanged.

10. Why are positron (β⁺) emitters used in PET scanning?

1. Positrons make tissue itself radioactive
2. Positrons are heavier than electrons so are easier to detect
3. Positrons pass straight out of the body to the detector
4. Each positron annihilates, producing two gamma photons in opposite directions

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D: Each positron annihilates, producing two gamma photons in opposite directions. A positron meets an electron and annihilates, giving two gamma photons travelling in opposite directions. Detecting them locates the source. Positrons themselves are absorbed within millimetres.