MYP · 17 · extended response
Inferring discrete levels from a line spectrum
Atomic and nuclear physics · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- discriminating
- Marks
- 6
- Topics
- 1
- Answer
- Complete
Idealised energy levels
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Energy / eV
Horizontal axis (x): Level index
Read the exact data as a table
| Level index | Energy / eV |
|---|---|
| 1 | -6 |
| 2 | -3 |
| 3 | -1.5 |
These are the supplied values, not a worked answer. No fitted trend is drawn.
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. An idealised atom has the supplied energy levels relative to ionisation at 0 eV. Use h = 4.14×10⁻¹⁵ eV s and c = 3.0×10⁸ m s⁻¹. The atom initially occupies the −1.5 eV level; allowed transitions between all listed levels may emit photons. Supplied data (Level index; Energy / eV): (1, -6), (2, -3), (3, -1.5).
- (a)
List the possible emitted photon energies in cascades and find the shortest emitted wavelength.
3 marks - (b)
From the −6.0 eV ground level, can isolated 2.0 eV and 6.5 eV photons be absorbed? Explain what line spectra establish about the model.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
List the possible emitted photon energies in cascades and find the shortest emitted wavelength.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
Energy drops are (−1.5)−(−3.0)=1.5 eV, (−3.0)−(−6.0)=3.0 eV and (−1.5)−(−6.0)=4.5 eV.
- 2
A direct transition emits one 4.5 eV photon; a two-step cascade emits separate 1.5 and 3.0 eV photons, not one of each plus 4.5 eV in the same decay.
- 3
The greatest photon energy gives shortest wavelength: λ = hc/E = (4.14×10⁻¹⁵)(3.0×10⁸)/4.5≈2.76×10⁻⁷ m.
(b)
From the −6.0 eV ground level, can isolated 2.0 eV and 6.5 eV photons be absorbed? Explain what line spectra establish about the model.
Build a chain of claim, evidence and physics reasoning. Address more than one relevant factor, identify a limitation or assumption, and finish with a conclusion that is conditional on the evidence rather than absolute.
- 1
A bound–bound absorption must match an allowed energy difference; the listed ground-state excitation gaps are 3.0 and 4.5 eV, not 2.0 eV.
- 2
Ground-state ionisation needs 6.0 eV. Absorbing 6.5 eV can free the electron with 0.5 eV excess kinetic energy, neglecting recoil.
- 3
Discrete lines support quantised energy changes. They do not show electrons following literal tiny planetary trajectories, and a real atom may have selection rules absent from this idealised model.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- Energy drops are (−1.5)−(−3.0)=1.5 eV, (−3.0)−(−6.0)=3.0 eV and (−1.5)−(−6.0)=4.5 eV.
- A direct transition emits one 4.5 eV photon; a two-step cascade emits separate 1.5 and 3.0 eV photons, not one of each plus 4.5 eV in the same decay.
- The greatest photon energy gives shortest wavelength: λ = hc/E = (4.14×10⁻¹⁵)(3.0×10⁸)/4.5≈2.76×10⁻⁷ m.
- A bound–bound absorption must match an allowed energy difference; the listed ground-state excitation gaps are 3.0 and 4.5 eV, not 2.0 eV.
- Ground-state ionisation needs 6.0 eV. Absorbing 6.5 eV can free the electron with 0.5 eV excess kinetic energy, neglecting recoil.
- Discrete lines support quantised energy changes. They do not show electrons following literal tiny planetary trajectories, and a real atom may have selection rules absent from this idealised model.
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