IB · PHYSICS HL

Physics: Higher Level

Quantum physics — HL Theme E

Name: ____________________Date: October 10, 2026

1.
Light of frequency 7.5 × 10¹⁴ Hz is incident on a metal surface with work function 2.5 × 10⁻¹⁹ J. Calculate the maximum kinetic energy of the emitted photoelectrons. Use h = 6.63 × 10⁻³⁴ J s.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses the photoelectric equation hf = Φ + EKmax. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Calculates the photon energy hf = (6.63 × 10⁻³⁴)(7.5 × 10¹⁴) ≈ 4.97 × 10⁻¹⁹ J. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Rearranges to EKmax = hf − Φ. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: Obtains EKmax ≈ 2.47 × 10⁻¹⁹ J. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The work function is the minimum energy needed to remove an electron; any photon energy beyond it becomes the electron's kinetic energy, not additional removed electrons.
Marking points
- Uses the photoelectric equation hf = Φ + EKmax.
- Calculates the photon energy hf = (6.63 × 10⁻³⁴)(7.5 × 10¹⁴) ≈ 4.97 × 10⁻¹⁹ J.
- Rearranges to EKmax = hf − Φ.
- Obtains EKmax ≈ 2.47 × 10⁻¹⁹ J.
Examiner tip: The work function is the minimum energy needed to remove an electron; any photon energy beyond it becomes the electron's kinetic energy, not additional removed electrons.
2.
Marking analysis: A learner attempts the following task: “Light of frequency 7.5 × 10¹⁴ Hz is incident on a metal surface with work function 2.5 × 10⁻¹⁹ J. Calculate the maximum kinetic energy of the emitted photoelectrons. Use h = 6.63 × 10⁻³⁴ J s.” Their response addresses only this point: “Uses the photoelectric equation hf = Φ + EKmax.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses the photoelectric equation hf = Φ + EKmax. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Calculates the photon energy hf = (6.63 × 10⁻³⁴)(7.5 × 10¹⁴) ≈ 4.97 × 10⁻¹⁹ J. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Rearranges to EKmax = hf − Φ. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Obtains EKmax ≈ 2.47 × 10⁻¹⁹ J. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses the photoelectric equation hf = Φ + EKmax.
- Identifies the missing requirement: Calculates the photon energy hf = (6.63 × 10⁻³⁴)(7.5 × 10¹⁴) ≈ 4.97 × 10⁻¹⁹ J.
- Identifies the missing requirement: Rearranges to EKmax = hf − Φ.
- Identifies the missing requirement: Obtains EKmax ≈ 2.47 × 10⁻¹⁹ J.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
3.
Explain how the photoelectric effect provides evidence for the particle nature of light, referring to the observation that emission is instantaneous and depends on frequency rather than intensity.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that wave theory predicts emission should depend on intensity (wave energy) and should show a time delay for energy to accumulate, neither of which is observed. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that below a threshold frequency, no electrons are emitted regardless of intensity, which wave theory cannot explain. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Work through this mathematical step: States that in the photon model, each photon carries discrete energy E = hf, and a single photon-electron interaction either has enough energy to eject an electron or it does not — explaining the instantaneous, frequency-dependent threshold. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: Concludes that this evidence supports light behaving as discrete quanta (photons) rather than a continuous wave in this interaction. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The threshold frequency and instantaneous emission are the two specific observations that classical wave theory fails to explain — always cite both when answering this classic question.
Marking points
- States that wave theory predicts emission should depend on intensity (wave energy) and should show a time delay for energy to accumulate, neither of which is observed.
- States that below a threshold frequency, no electrons are emitted regardless of intensity, which wave theory cannot explain.
- States that in the photon model, each photon carries discrete energy E = hf, and a single photon-electron interaction either has enough energy to eject an electron or it does not — explaining the instantaneous, frequency-dependent threshold.
- Concludes that this evidence supports light behaving as discrete quanta (photons) rather than a continuous wave in this interaction.
Examiner tip: The threshold frequency and instantaneous emission are the two specific observations that classical wave theory fails to explain — always cite both when answering this classic question.
4.
Marking analysis: A learner attempts the following task: “Explain how the photoelectric effect provides evidence for the particle nature of light, referring to the observation that emission is instantaneous and depends on frequency rather than intensity.” Their response addresses only this point: “States that wave theory predicts emission should depend on intensity (wave energy) and should show a time delay for energy to accumulate, neither of which is observed.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that wave theory predicts emission should depend on intensity (wave energy) and should show a time delay for energy to accumulate, neither of which is observed. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that below a threshold frequency, no electrons are emitted regardless of intensity, which wave theory cannot explain. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that in the photon model, each photon carries discrete energy E = hf, and a single photon-electron interaction either has enough energy to eject an electron or it does not — explaining the instantaneous, frequency-dependent threshold. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Concludes that this evidence supports light behaving as discrete quanta (photons) rather than a continuous wave in this interaction. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that wave theory predicts emission should depend on intensity (wave energy) and should show a time delay for energy to accumulate, neither of which is observed.
- Identifies the missing requirement: States that below a threshold frequency, no electrons are emitted regardless of intensity, which wave theory cannot explain.
- Identifies the missing requirement: States that in the photon model, each photon carries discrete energy E = hf, and a single photon-electron interaction either has enough energy to eject an electron or it does not — explaining the instantaneous, frequency-dependent threshold.
- Identifies the missing requirement: Concludes that this evidence supports light behaving as discrete quanta (photons) rather than a continuous wave in this interaction.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
5.
Calculate the de Broglie wavelength of an electron (mass 9.11 × 10⁻³¹ kg) travelling at 2.0 × 10⁶ m s⁻¹. Use h = 6.63 × 10⁻³⁴ J s.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses λ = h/(mv). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes λ = (6.63 × 10⁻³⁴)/((9.11 × 10⁻³¹)(2.0 × 10⁶)). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: Obtains λ ≈ 3.64 × 10⁻¹⁰ m. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The de Broglie relation applies to any moving particle with momentum, not just photons — this wavelength is on the scale of atomic spacing, which is why electron diffraction by crystals is observable.
Marking points
- Uses λ = h/(mv).
- Substitutes λ = (6.63 × 10⁻³⁴)/((9.11 × 10⁻³¹)(2.0 × 10⁶)).
- Obtains λ ≈ 3.64 × 10⁻¹⁰ m.
Examiner tip: The de Broglie relation applies to any moving particle with momentum, not just photons — this wavelength is on the scale of atomic spacing, which is why electron diffraction by crystals is observable.
6.
Marking analysis: A learner attempts the following task: “Calculate the de Broglie wavelength of an electron (mass 9.11 × 10⁻³¹ kg) travelling at 2.0 × 10⁶ m s⁻¹. Use h = 6.63 × 10⁻³⁴ J s.” Their response addresses only this point: “Uses λ = h/(mv).” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses λ = h/(mv). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Substitutes λ = (6.63 × 10⁻³⁴)/((9.11 × 10⁻³¹)(2.0 × 10⁶)). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Obtains λ ≈ 3.64 × 10⁻¹⁰ m. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses λ = h/(mv).
- Identifies the missing requirement: Substitutes λ = (6.63 × 10⁻³⁴)/((9.11 × 10⁻³¹)(2.0 × 10⁶)).
- Identifies the missing requirement: Obtains λ ≈ 3.64 × 10⁻¹⁰ m.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
7.
Explain what electron diffraction experiments demonstrate about the nature of matter, and state one practical device that relies on this wave-like behaviour of electrons.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that electron diffraction produces interference patterns, a behaviour characteristic of waves, when electrons pass through a crystal or thin film. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that this demonstrates matter (normally considered particles) exhibits wave-like properties, supporting wave-particle duality. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States a practical application, e.g. the electron microscope, which uses electron wavelengths (much shorter than visible light) to achieve much higher resolution. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Wave-particle duality applies to all matter and radiation; electrons showing diffraction is the matter-side evidence, paralleling the photoelectric effect as the radiation-side evidence for particle behaviour.
Marking points
- States that electron diffraction produces interference patterns, a behaviour characteristic of waves, when electrons pass through a crystal or thin film.
- States that this demonstrates matter (normally considered particles) exhibits wave-like properties, supporting wave-particle duality.
- States a practical application, e.g. the electron microscope, which uses electron wavelengths (much shorter than visible light) to achieve much higher resolution.
Examiner tip: Wave-particle duality applies to all matter and radiation; electrons showing diffraction is the matter-side evidence, paralleling the photoelectric effect as the radiation-side evidence for particle behaviour.
8.
Marking analysis: A learner attempts the following task: “Explain what electron diffraction experiments demonstrate about the nature of matter, and state one practical device that relies on this wave-like behaviour of electrons.” Their response addresses only this point: “States that electron diffraction produces interference patterns, a behaviour characteristic of waves, when electrons pass through a crystal or thin film.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that electron diffraction produces interference patterns, a behaviour characteristic of waves, when electrons pass through a crystal or thin film. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that this demonstrates matter (normally considered particles) exhibits wave-like properties, supporting wave-particle duality. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States a practical application, e.g. the electron microscope, which uses electron wavelengths (much shorter than visible light) to achieve much higher resolution. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that electron diffraction produces interference patterns, a behaviour characteristic of waves, when electrons pass through a crystal or thin film.
- Identifies the missing requirement: States that this demonstrates matter (normally considered particles) exhibits wave-like properties, supporting wave-particle duality.
- Identifies the missing requirement: States a practical application, e.g. the electron microscope, which uses electron wavelengths (much shorter than visible light) to achieve much higher resolution.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
9.
An electron in a hydrogen atom transitions from an energy level of −1.51 eV to a level of −3.40 eV, emitting a photon. Calculate the energy and frequency of the emitted photon. Use h = 6.63 × 10⁻³⁴ J s and 1 eV = 1.60 × 10⁻¹⁹ J.
[5 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Calculates the energy released: ΔE = (−1.51) − (−3.40) = 1.89 eV. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Develop this part of the answer: Converts to joules: 1.89 × 1.60 × 10⁻¹⁹ ≈ 3.02 × 10⁻¹⁹ J. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Work through this mathematical step: States that this energy equals the photon energy: Ephoton = hf. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Rearranges to f = E/h. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Develop this part of the answer: Obtains f ≈ 4.56 × 10¹⁴ Hz. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
7. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: A transition from a higher (less negative) to a lower (more negative) energy level releases a photon; convert eV to joules before using hf, since h is given in SI units.
Marking points
- Calculates the energy released: ΔE = (−1.51) − (−3.40) = 1.89 eV.
- Converts to joules: 1.89 × 1.60 × 10⁻¹⁹ ≈ 3.02 × 10⁻¹⁹ J.
- States that this energy equals the photon energy: Ephoton = hf.
- Rearranges to f = E/h.
- Obtains f ≈ 4.56 × 10¹⁴ Hz.
Examiner tip: A transition from a higher (less negative) to a lower (more negative) energy level releases a photon; convert eV to joules before using hf, since h is given in SI units.
10.
Marking analysis: A learner attempts the following task: “An electron in a hydrogen atom transitions from an energy level of −1.51 eV to a level of −3.40 eV, emitting a photon. Calculate the energy and frequency of the emitted photon. Use h = 6.63 × 10⁻³⁴ J s and 1 eV = 1.60 × 10⁻¹⁹ J.” Their response addresses only this point: “Calculates the energy released: ΔE = (−1.51) − (−3.40) = 1.89 eV.” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[5 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Calculates the energy released: ΔE = (−1.51) − (−3.40) = 1.89 eV. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Converts to joules: 1.89 × 1.60 × 10⁻¹⁹ ≈ 3.02 × 10⁻¹⁹ J. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that this energy equals the photon energy: Ephoton = hf. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Rearranges to f = E/h. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Requirement 5: Identifies the missing requirement: Obtains f ≈ 4.56 × 10¹⁴ Hz. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
7. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Calculates the energy released: ΔE = (−1.51) − (−3.40) = 1.89 eV.
- Identifies the missing requirement: Converts to joules: 1.89 × 1.60 × 10⁻¹⁹ ≈ 3.02 × 10⁻¹⁹ J.
- Identifies the missing requirement: States that this energy equals the photon energy: Ephoton = hf.
- Identifies the missing requirement: Rearranges to f = E/h.
- Identifies the missing requirement: Obtains f ≈ 4.56 × 10¹⁴ Hz.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
11.
Explain why atomic emission spectra consist of discrete lines rather than a continuous range of wavelengths, in terms of electron energy levels.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that electrons in an atom can only occupy specific, discrete (quantised) energy levels. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that a photon is emitted only when an electron transitions between two specific energy levels, with photon energy equal to the exact energy difference. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that since only specific energy differences are possible, only specific photon frequencies (and hence wavelengths) can be emitted, producing discrete spectral lines. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Each spectral line corresponds to one specific electron transition between two energy levels — the discreteness of the spectrum directly reflects the discreteness (quantisation) of atomic energy levels.
Marking points
- States that electrons in an atom can only occupy specific, discrete (quantised) energy levels.
- States that a photon is emitted only when an electron transitions between two specific energy levels, with photon energy equal to the exact energy difference.
- States that since only specific energy differences are possible, only specific photon frequencies (and hence wavelengths) can be emitted, producing discrete spectral lines.
Examiner tip: Each spectral line corresponds to one specific electron transition between two energy levels — the discreteness of the spectrum directly reflects the discreteness (quantisation) of atomic energy levels.
12.
Marking analysis: A learner attempts the following task: “Explain why atomic emission spectra consist of discrete lines rather than a continuous range of wavelengths, in terms of electron energy levels.” Their response addresses only this point: “States that electrons in an atom can only occupy specific, discrete (quantised) energy levels.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that electrons in an atom can only occupy specific, discrete (quantised) energy levels. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that a photon is emitted only when an electron transitions between two specific energy levels, with photon energy equal to the exact energy difference. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that since only specific energy differences are possible, only specific photon frequencies (and hence wavelengths) can be emitted, producing discrete spectral lines. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that electrons in an atom can only occupy specific, discrete (quantised) energy levels.
- Identifies the missing requirement: States that a photon is emitted only when an electron transitions between two specific energy levels, with photon energy equal to the exact energy difference.
- Identifies the missing requirement: States that since only specific energy differences are possible, only specific photon frequencies (and hence wavelengths) can be emitted, producing discrete spectral lines.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
13.
The Heisenberg uncertainty principle can be expressed as ΔxΔp ≥ h/4π. Explain what this principle states about simultaneously measuring the position and momentum of a particle.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that it is fundamentally impossible to know both the exact position and exact momentum of a particle simultaneously. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that Δx and Δp represent the uncertainties (not measurement errors) in position and momentum respectively. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that reducing the uncertainty in position (more precise position) necessarily increases the uncertainty in momentum, and vice versa. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: This is a fundamental property of nature, not a limitation of measuring instruments — even a perfect instrument cannot beat this limit.
Marking points
- States that it is fundamentally impossible to know both the exact position and exact momentum of a particle simultaneously.
- States that Δx and Δp represent the uncertainties (not measurement errors) in position and momentum respectively.
- States that reducing the uncertainty in position (more precise position) necessarily increases the uncertainty in momentum, and vice versa.
Examiner tip: This is a fundamental property of nature, not a limitation of measuring instruments — even a perfect instrument cannot beat this limit.
14.
Marking analysis: A learner attempts the following task: “The Heisenberg uncertainty principle can be expressed as ΔxΔp ≥ h/4π. Explain what this principle states about simultaneously measuring the position and momentum of a particle.” Their response addresses only this point: “States that it is fundamentally impossible to know both the exact position and exact momentum of a particle simultaneously.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that it is fundamentally impossible to know both the exact position and exact momentum of a particle simultaneously. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that Δx and Δp represent the uncertainties (not measurement errors) in position and momentum respectively. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that reducing the uncertainty in position (more precise position) necessarily increases the uncertainty in momentum, and vice versa. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that it is fundamentally impossible to know both the exact position and exact momentum of a particle simultaneously.
- Identifies the missing requirement: States that Δx and Δp represent the uncertainties (not measurement errors) in position and momentum respectively.
- Identifies the missing requirement: States that reducing the uncertainty in position (more precise position) necessarily increases the uncertainty in momentum, and vice versa.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
15.
A nucleus in an excited state has energy 4.8 MeV above its ground state and decays by emitting a gamma-ray photon. Calculate the wavelength of the emitted gamma ray. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Develop this part of the answer: Converts the energy to joules: 4.8 × 10⁶ × 1.60 × 10⁻¹⁹ ≈ 7.68 × 10⁻¹³ J. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Work through this mathematical step: Uses E = hc/λ. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Rearranges to λ = hc/E. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: Obtains λ ≈ 2.59 × 10⁻¹³ m. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Nuclear energy-level transitions follow the same E = hc/λ relationship as atomic transitions, but with energies roughly a million times larger, giving gamma-ray (not visible-light) wavelengths.
Marking points
- Converts the energy to joules: 4.8 × 10⁶ × 1.60 × 10⁻¹⁹ ≈ 7.68 × 10⁻¹³ J.
- Uses E = hc/λ.
- Rearranges to λ = hc/E.
- Obtains λ ≈ 2.59 × 10⁻¹³ m.
Examiner tip: Nuclear energy-level transitions follow the same E = hc/λ relationship as atomic transitions, but with energies roughly a million times larger, giving gamma-ray (not visible-light) wavelengths.
16.
Marking analysis: A learner attempts the following task: “A nucleus in an excited state has energy 4.8 MeV above its ground state and decays by emitting a gamma-ray photon. Calculate the wavelength of the emitted gamma ray. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.” Their response addresses only this point: “Converts the energy to joules: 4.8 × 10⁶ × 1.60 × 10⁻¹⁹ ≈ 7.68 × 10⁻¹³ J.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Converts the energy to joules: 4.8 × 10⁶ × 1.60 × 10⁻¹⁹ ≈ 7.68 × 10⁻¹³ J. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Uses E = hc/λ. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Rearranges to λ = hc/E. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Obtains λ ≈ 2.59 × 10⁻¹³ m. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Converts the energy to joules: 4.8 × 10⁶ × 1.60 × 10⁻¹⁹ ≈ 7.68 × 10⁻¹³ J.
- Identifies the missing requirement: Uses E = hc/λ.
- Identifies the missing requirement: Rearranges to λ = hc/E.
- Identifies the missing requirement: Obtains λ ≈ 2.59 × 10⁻¹³ m.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
17.
Distinguish between a continuous emission spectrum and a line absorption spectrum, and state the conditions under which each is produced.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that a continuous spectrum contains all wavelengths across a range and is produced by a hot, dense source such as a solid, liquid, or dense gas (e.g. a filament lamp). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that a line absorption spectrum shows dark lines at specific wavelengths superimposed on a continuous background. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that this occurs when continuous-spectrum light passes through a cooler, low-density gas, which absorbs specific wavelengths corresponding to its atoms' allowed energy transitions. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The dark lines in an absorption spectrum occur at exactly the same wavelengths as the bright lines in that element's emission spectrum, since both correspond to the same set of allowed energy transitions.
Marking points
- States that a continuous spectrum contains all wavelengths across a range and is produced by a hot, dense source such as a solid, liquid, or dense gas (e.g. a filament lamp).
- States that a line absorption spectrum shows dark lines at specific wavelengths superimposed on a continuous background.
- States that this occurs when continuous-spectrum light passes through a cooler, low-density gas, which absorbs specific wavelengths corresponding to its atoms' allowed energy transitions.
Examiner tip: The dark lines in an absorption spectrum occur at exactly the same wavelengths as the bright lines in that element's emission spectrum, since both correspond to the same set of allowed energy transitions.
18.
Marking analysis: A learner attempts the following task: “Distinguish between a continuous emission spectrum and a line absorption spectrum, and state the conditions under which each is produced.” Their response addresses only this point: “States that a continuous spectrum contains all wavelengths across a range and is produced by a hot, dense source such as a solid, liquid, or dense gas (e.g. a filament lamp).” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that a continuous spectrum contains all wavelengths across a range and is produced by a hot, dense source such as a solid, liquid, or dense gas (e.g. a filament lamp). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that a line absorption spectrum shows dark lines at specific wavelengths superimposed on a continuous background. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that this occurs when continuous-spectrum light passes through a cooler, low-density gas, which absorbs specific wavelengths corresponding to its atoms' allowed energy transitions. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that a continuous spectrum contains all wavelengths across a range and is produced by a hot, dense source such as a solid, liquid, or dense gas (e.g. a filament lamp).
- Identifies the missing requirement: States that a line absorption spectrum shows dark lines at specific wavelengths superimposed on a continuous background.
- Identifies the missing requirement: States that this occurs when continuous-spectrum light passes through a cooler, low-density gas, which absorbs specific wavelengths corresponding to its atoms' allowed energy transitions.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
19.
In an experiment, electrons are accelerated through a potential difference of 150 V before striking a target. Calculate the de Broglie wavelength of these electrons. Use e = 1.60 × 10⁻¹⁹ C, mₑ = 9.11 × 10⁻³¹ kg and h = 6.63 × 10⁻³⁴ J s.
[5 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses the work-energy relationship: eV = ½mv², so kinetic energy = eV. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Calculates the kinetic energy: (1.60 × 10⁻¹⁹)(150) = 2.4 × 10⁻¹⁷ J. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Rearranges ½mv² = EK to find v = √(2EK/m). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Work through this mathematical step: Calculates v ≈ 7.25 × 10⁶ m s⁻¹, then uses λ = h/(mv). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Develop this part of the answer: Obtains λ ≈ 1.00 × 10⁻¹⁰ m. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
7. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Accelerating electrons through a potential difference gives them kinetic energy eV; this must be converted to speed before applying the de Broglie relation, which needs momentum (mv), not energy directly.
Marking points
- Uses the work-energy relationship: eV = ½mv², so kinetic energy = eV.
- Calculates the kinetic energy: (1.60 × 10⁻¹⁹)(150) = 2.4 × 10⁻¹⁷ J.
- Rearranges ½mv² = EK to find v = √(2EK/m).
- Calculates v ≈ 7.25 × 10⁶ m s⁻¹, then uses λ = h/(mv).
- Obtains λ ≈ 1.00 × 10⁻¹⁰ m.
Examiner tip: Accelerating electrons through a potential difference gives them kinetic energy eV; this must be converted to speed before applying the de Broglie relation, which needs momentum (mv), not energy directly.
20.
Marking analysis: A learner attempts the following task: “In an experiment, electrons are accelerated through a potential difference of 150 V before striking a target. Calculate the de Broglie wavelength of these electrons. Use e = 1.60 × 10⁻¹⁹ C, mₑ = 9.11 × 10⁻³¹ kg and h = 6.63 × 10⁻³⁴ J s.” Their response addresses only this point: “Uses the work-energy relationship: eV = ½mv², so kinetic energy = eV.” Evaluate the response against the complete 5-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[5 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses the work-energy relationship: eV = ½mv², so kinetic energy = eV. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Calculates the kinetic energy: (1.60 × 10⁻¹⁹)(150) = 2.4 × 10⁻¹⁷ J. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Rearranges ½mv² = EK to find v = √(2EK/m). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Calculates v ≈ 7.25 × 10⁶ m s⁻¹, then uses λ = h/(mv). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Requirement 5: Identifies the missing requirement: Obtains λ ≈ 1.00 × 10⁻¹⁰ m. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
7. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses the work-energy relationship: eV = ½mv², so kinetic energy = eV.
- Identifies the missing requirement: Calculates the kinetic energy: (1.60 × 10⁻¹⁹)(150) = 2.4 × 10⁻¹⁷ J.
- Identifies the missing requirement: Rearranges ½mv² = EK to find v = √(2EK/m).
- Identifies the missing requirement: Calculates v ≈ 7.25 × 10⁶ m s⁻¹, then uses λ = h/(mv).
- Identifies the missing requirement: Obtains λ ≈ 1.00 × 10⁻¹⁰ m.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
21.
Distinguish between the Bohr model and the Schrödinger (quantum mechanical) model of the atom, in terms of how each describes the position of an electron.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that in the Bohr model, electrons orbit the nucleus in fixed, well-defined circular paths (orbits) at specific radii. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that in the Schrödinger model, an electron's position cannot be precisely known or predicted; instead it is described by a wavefunction giving the probability of finding the electron at a given location (an electron cloud or orbital). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that the Schrödinger model is consistent with the Heisenberg uncertainty principle, whereas the Bohr model's precisely defined orbits are not. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The Bohr model correctly predicts hydrogen's energy levels but incorrectly implies precisely knowable electron paths — the Schrödinger model keeps the quantised energy levels while replacing fixed orbits with probability distributions.
Marking points
- States that in the Bohr model, electrons orbit the nucleus in fixed, well-defined circular paths (orbits) at specific radii.
- States that in the Schrödinger model, an electron's position cannot be precisely known or predicted; instead it is described by a wavefunction giving the probability of finding the electron at a given location (an electron cloud or orbital).
- States that the Schrödinger model is consistent with the Heisenberg uncertainty principle, whereas the Bohr model's precisely defined orbits are not.
Examiner tip: The Bohr model correctly predicts hydrogen's energy levels but incorrectly implies precisely knowable electron paths — the Schrödinger model keeps the quantised energy levels while replacing fixed orbits with probability distributions.
22.
Marking analysis: A learner attempts the following task: “Distinguish between the Bohr model and the Schrödinger (quantum mechanical) model of the atom, in terms of how each describes the position of an electron.” Their response addresses only this point: “States that in the Bohr model, electrons orbit the nucleus in fixed, well-defined circular paths (orbits) at specific radii.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that in the Bohr model, electrons orbit the nucleus in fixed, well-defined circular paths (orbits) at specific radii. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that in the Schrödinger model, an electron's position cannot be precisely known or predicted; instead it is described by a wavefunction giving the probability of finding the electron at a given location (an electron cloud or orbital). Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States that the Schrödinger model is consistent with the Heisenberg uncertainty principle, whereas the Bohr model's precisely defined orbits are not. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that in the Bohr model, electrons orbit the nucleus in fixed, well-defined circular paths (orbits) at specific radii.
- Identifies the missing requirement: States that in the Schrödinger model, an electron's position cannot be precisely known or predicted; instead it is described by a wavefunction giving the probability of finding the electron at a given location (an electron cloud or orbital).
- Identifies the missing requirement: States that the Schrödinger model is consistent with the Heisenberg uncertainty principle, whereas the Bohr model's precisely defined orbits are not.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
23.
Calculate the momentum of a photon of wavelength 500 nm. Use h = 6.63 × 10⁻³⁴ J s.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses p = h/λ. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Converts wavelength to metres: 500 nm = 5.00 × 10⁻⁷ m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Substitutes p = (6.63 × 10⁻³⁴)/(5.00 × 10⁻⁷) to obtain p ≈ 1.33 × 10⁻²⁷ kg m s⁻¹. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: A photon has zero rest mass but still carries momentum, given by p = h/λ (equivalently p = E/c) — this is essential to explaining phenomena like radiation pressure and Compton scattering.
Marking points
- Uses p = h/λ.
- Converts wavelength to metres: 500 nm = 5.00 × 10⁻⁷ m.
- Substitutes p = (6.63 × 10⁻³⁴)/(5.00 × 10⁻⁷) to obtain p ≈ 1.33 × 10⁻²⁷ kg m s⁻¹.
Examiner tip: A photon has zero rest mass but still carries momentum, given by p = h/λ (equivalently p = E/c) — this is essential to explaining phenomena like radiation pressure and Compton scattering.
24.
Marking analysis: A learner attempts the following task: “Calculate the momentum of a photon of wavelength 500 nm. Use h = 6.63 × 10⁻³⁴ J s.” Their response addresses only this point: “Uses p = h/λ.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: Uses p = h/λ. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Converts wavelength to metres: 500 nm = 5.00 × 10⁻⁷ m. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Substitutes p = (6.63 × 10⁻³⁴)/(5.00 × 10⁻⁷) to obtain p ≈ 1.33 × 10⁻²⁷ kg m s⁻¹. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: Uses p = h/λ.
- Identifies the missing requirement: Converts wavelength to metres: 500 nm = 5.00 × 10⁻⁷ m.
- Identifies the missing requirement: Substitutes p = (6.63 × 10⁻³⁴)/(5.00 × 10⁻⁷) to obtain p ≈ 1.33 × 10⁻²⁷ kg m s⁻¹.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
25.
A metal has a work function of 3.5 × 10⁻¹⁹ J. Calculate the threshold frequency for the photoelectric effect to occur at this surface. Use h = 6.63 × 10⁻³⁴ J s.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: States that at the threshold frequency, EKmax = 0, so hf₀ = Φ. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Rearranges to f₀ = Φ/h. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Substitutes f₀ = (3.5 × 10⁻¹⁹)/(6.63 × 10⁻³⁴) to obtain f₀ ≈ 5.28 × 10¹⁴ Hz. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The threshold frequency is the minimum photon frequency capable of ejecting an electron at all — below it, no photoelectrons are emitted no matter how intense the light.
Marking points
- States that at the threshold frequency, EKmax = 0, so hf₀ = Φ.
- Rearranges to f₀ = Φ/h.
- Substitutes f₀ = (3.5 × 10⁻¹⁹)/(6.63 × 10⁻³⁴) to obtain f₀ ≈ 5.28 × 10¹⁴ Hz.
Examiner tip: The threshold frequency is the minimum photon frequency capable of ejecting an electron at all — below it, no photoelectrons are emitted no matter how intense the light.
26.
Marking analysis: A learner attempts the following task: “A metal has a work function of 3.5 × 10⁻¹⁹ J. Calculate the threshold frequency for the photoelectric effect to occur at this surface. Use h = 6.63 × 10⁻³⁴ J s.” Their response addresses only this point: “States that at the threshold frequency, EKmax = 0, so hf₀ = Φ.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that at the threshold frequency, EKmax = 0, so hf₀ = Φ. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: Rearranges to f₀ = Φ/h. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Substitutes f₀ = (3.5 × 10⁻¹⁹)/(6.63 × 10⁻³⁴) to obtain f₀ ≈ 5.28 × 10¹⁴ Hz. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that at the threshold frequency, EKmax = 0, so hf₀ = Φ.
- Identifies the missing requirement: Rearranges to f₀ = Φ/h.
- Identifies the missing requirement: Substitutes f₀ = (3.5 × 10⁻¹⁹)/(6.63 × 10⁻³⁴) to obtain f₀ ≈ 5.28 × 10¹⁴ Hz.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
27.
State the minimum photon energy required for pair production (in which a photon converts into an electron and a positron) to occur, in terms of the rest mass of an electron, mₑ, and calculate this minimum energy in joules. Use c = 3.00 × 10⁸ m s⁻¹ and mₑ = 9.11 × 10⁻³¹ kg.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Develop this part of the answer: States that pair production requires the photon energy to be at least enough to create the rest mass energy of both the electron and the positron produced. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States the minimum energy as 2mₑc². Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Work through this mathematical step: Substitutes 2 × (9.11 × 10⁻³¹) × (3.00 × 10⁸)². Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: Obtains minimum energy ≈ 1.64 × 10⁻¹³ J. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Pair production and annihilation are mirror processes: a photon of at least 2mₑc² can create an electron-positron pair, and an electron-positron pair colliding annihilates to produce photons of the same total energy.
Marking points
- States that pair production requires the photon energy to be at least enough to create the rest mass energy of both the electron and the positron produced.
- States the minimum energy as 2mₑc².
- Substitutes 2 × (9.11 × 10⁻³¹) × (3.00 × 10⁸)².
- Obtains minimum energy ≈ 1.64 × 10⁻¹³ J.
Examiner tip: Pair production and annihilation are mirror processes: a photon of at least 2mₑc² can create an electron-positron pair, and an electron-positron pair colliding annihilates to produce photons of the same total energy.
28.
Marking analysis: A learner attempts the following task: “State the minimum photon energy required for pair production (in which a photon converts into an electron and a positron) to occur, in terms of the rest mass of an electron, mₑ, and calculate this minimum energy in joules. Use c = 3.00 × 10⁸ m s⁻¹ and mₑ = 9.11 × 10⁻³¹ kg.” Their response addresses only this point: “States that pair production requires the photon energy to be at least enough to create the rest mass energy of both the electron and the positron produced.” Evaluate the response against the complete 4-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that pair production requires the photon energy to be at least enough to create the rest mass energy of both the electron and the positron produced. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States the minimum energy as 2mₑc². Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: Substitutes 2 × (9.11 × 10⁻³¹) × (3.00 × 10⁸)². Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Requirement 4: Identifies the missing requirement: Obtains minimum energy ≈ 1.64 × 10⁻¹³ J. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that pair production requires the photon energy to be at least enough to create the rest mass energy of both the electron and the positron produced.
- Identifies the missing requirement: States the minimum energy as 2mₑc².
- Identifies the missing requirement: Substitutes 2 × (9.11 × 10⁻³¹) × (3.00 × 10⁸)².
- Identifies the missing requirement: Obtains minimum energy ≈ 1.64 × 10⁻¹³ J.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
29.
Explain what is meant by quantum tunnelling, and state one physical phenomenon or application that relies on it.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that quantum tunnelling is the phenomenon in which a particle has a non-zero probability of passing through a potential energy barrier, even when the particle's energy is less than the height of the barrier — a situation forbidden in classical physics. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that this is explained by treating the particle's wavefunction as extending, with reduced but non-zero amplitude, into and beyond the barrier region. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States a valid application, e.g. alpha decay, in which an alpha particle tunnels through the nuclear potential barrier, or the scanning tunnelling microscope. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Quantum tunnelling has no classical analogue at all — it is a direct, observable consequence of treating particles as having a wave nature, with a wavefunction that does not simply stop at a barrier's edge.
Marking points
- States that quantum tunnelling is the phenomenon in which a particle has a non-zero probability of passing through a potential energy barrier, even when the particle's energy is less than the height of the barrier — a situation forbidden in classical physics.
- States that this is explained by treating the particle's wavefunction as extending, with reduced but non-zero amplitude, into and beyond the barrier region.
- States a valid application, e.g. alpha decay, in which an alpha particle tunnels through the nuclear potential barrier, or the scanning tunnelling microscope.
Examiner tip: Quantum tunnelling has no classical analogue at all — it is a direct, observable consequence of treating particles as having a wave nature, with a wavefunction that does not simply stop at a barrier's edge.
30.
Marking analysis: A learner attempts the following task: “Explain what is meant by quantum tunnelling, and state one physical phenomenon or application that relies on it.” Their response addresses only this point: “States that quantum tunnelling is the phenomenon in which a particle has a non-zero probability of passing through a potential energy barrier, even when the particle's energy is less than the height of the barrier — a situation forbidden in classical physics.” Evaluate the response against the complete 3-mark task. Identify what earns credit and state every additional requirement needed for full marks.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Separate the learner's stated response from the complete task. Credit only what their response demonstrates, then identify each missing requirement; do not assume unstated working.
2. Requirement 1: Recognises credit for the stated point: States that quantum tunnelling is the phenomenon in which a particle has a non-zero probability of passing through a potential energy barrier, even when the particle's energy is less than the height of the barrier — a situation forbidden in classical physics. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
3. Requirement 2: Identifies the missing requirement: States that this is explained by treating the particle's wavefunction as extending, with reduced but non-zero amplitude, into and beyond the barrier region. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
4. Requirement 3: Identifies the missing requirement: States a valid application, e.g. alpha decay, in which an alpha particle tunnels through the nuclear potential barrier, or the scanning tunnelling microscope. Compare this requirement with the supplied learner response; missing evidence cannot earn credit.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.
Marking points
- Recognises credit for the stated point: States that quantum tunnelling is the phenomenon in which a particle has a non-zero probability of passing through a potential energy barrier, even when the particle's energy is less than the height of the barrier — a situation forbidden in classical physics.
- Identifies the missing requirement: States that this is explained by treating the particle's wavefunction as extending, with reduced but non-zero amplitude, into and beyond the barrier region.
- Identifies the missing requirement: States a valid application, e.g. alpha decay, in which an alpha particle tunnels through the nuclear potential barrier, or the scanning tunnelling microscope.
Examiner tip: Treat each marking point as a separate requirement. Do not award the same idea twice, and do not infer work the learner did not show.