Cambridge International AS & A Level · 22 · structured
Discrete energy levels and line spectra
Discrete energy levels and line spectra · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 10
- Topics
- 3
- Answer
- Complete
An idealised isolated atom has bound energy levels −6.0 eV, −3.0 eV and −1.0 eV; zero is the ionisation limit. Use h=6.63×10⁻³⁴ J s, c=3.00×10⁸ m s⁻¹ and 1 eV=1.60×10⁻¹⁹ J.
- (a)
Explain what is meant by discrete electron energy levels. For an atom initially at −6.0 eV, decide whether a 3.0 eV photon or a 4.0 eV photon can cause a bound-level absorption in this model.
3 marks - (b)
An atom falls from −1.0 eV to −3.0 eV. Calculate the emitted photon frequency and wavelength.
3 marks - (c)
Describe the appearance and formation of an emission line spectrum from excited low-pressure gas and an absorption line spectrum when continuum light passes through cooler gas.
4 marks
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(a)
Explain what is meant by discrete electron energy levels. For an atom initially at −6.0 eV, decide whether a 3.0 eV photon or a 4.0 eV photon can cause a bound-level absorption in this model.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
A bound electron cannot take any arbitrary energy between levels; the allowed atom energies form a discrete set.
- 2
Absorption needs a photon energy matching a permitted energy difference.
- 3
3.0 eV matches −6.0→−3.0 eV; 4.0 eV would end at −2.0 eV, which is not a permitted level here.
(b)
An atom falls from −1.0 eV to −3.0 eV. Calculate the emitted photon frequency and wavelength.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Photon energy is the positive gap E_high−E_low=(−1.0)−(−3.0)=2.0 eV=3.20×10⁻¹⁹ J.
- 2
f=ΔE/h=3.20×10⁻¹⁹/(6.63×10⁻³⁴)=4.83×10¹⁴ Hz.
- 3
λ=c/f=6.22×10⁻⁷ m, about 622 nm.
(c)
Describe the appearance and formation of an emission line spectrum from excited low-pressure gas and an absorption line spectrum when continuum light passes through cooler gas.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Excited gas emits photons when atoms make downward transitions; allowed gaps give bright lines at discrete wavelengths on a dark background.
- 2
Continuum light passing through cooler gas loses photons at selected wavelengths corresponding to upward transitions.
- 3
Those missing wavelengths appear as dark lines in the transmitted continuous spectrum.
- 4
Subsequent emission is in varied directions, so it does not simply restore all the removed photons to the original viewing beam.
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.
- (a) A bound electron cannot take any arbitrary energy between levels; the allowed atom energies form a discrete set.
- (a) Absorption needs a photon energy matching a permitted energy difference.
- (a) 3.0 eV matches −6.0→−3.0 eV; 4.0 eV would end at −2.0 eV, which is not a permitted level here.
- (b) Photon energy is the positive gap E_high−E_low=(−1.0)−(−3.0)=2.0 eV=3.20×10⁻¹⁹ J.
- (b) f=ΔE/h=3.20×10⁻¹⁹/(6.63×10⁻³⁴)=4.83×10¹⁴ Hz.
- (b) λ=c/f=6.22×10⁻⁷ m, about 622 nm.
- (c) Excited gas emits photons when atoms make downward transitions; allowed gaps give bright lines at discrete wavelengths on a dark background.
- (c) Continuum light passing through cooler gas loses photons at selected wavelengths corresponding to upward transitions.
- (c) Those missing wavelengths appear as dark lines in the transmitted continuous spectrum.
- (c) Subsequent emission is in varied directions, so it does not simply restore all the removed photons to the original viewing beam.
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