Quantum physics: evidence, states and spectra
Key idea: Keep evidence tied to the claim it supports, add probability amplitudes before probabilities, and derive quantised energies from boundary conditions rather than treating them as arbitrary rules.
Before you start: Waves and Superposition objective chainEnergy and Fields objective chain
By the end, you can
- Connect particle and wave evidence to photons, energy, momentum and matter waves.
- Interpret and normalise wavefunctions, use probability density and apply superposition.
- Apply position–momentum uncertainty and infinite-square-well standing-wave quantisation.
- Explain discrete atomic levels, distinguish line spectra and solve photon-transition problems.
Starting-point self-check
1. Check your starting point
Attempt all five groups without notes and mark the first evidence, amplitude, boundary, uncertainty or transition step you cannot justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Atomic energy levels and line spectra 19(k)–(m)
Question 1
Levels are −5.0 eV and −2.0 eV. State the photon energy for each transition direction and identify emission versus absorption.
Check the model response
The energy difference is 3.0 eV. Upward transition absorbs a 3.0 eV photon; downward transition emits one.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Atomic energy levels and line spectra 19(k)–(m)
Check this idea
Misconception: An atom can absorb any photon above a minimum energy.
Repair: An isolated atom absorbs photons matching allowed upward level differences.
Check this idea
Misconception: Emission and absorption lines come from unrelated energies.
Repair: They correspond to the same level differences in opposite transition directions.
worked example
3. Follow five worked models
Follow how each solution ties evidence to a claim, normalises amplitudes, applies boundary conditions or selects an allowed transition.
Atomic energy levels and line spectra 19(k)–(m)
Model 1
An atom drops by 4.0 eV. Find emitted wavelength using hc = 1240 eV nm and relate it to a spectrum.
Check the model response
λ = 1240/4.0 = 310 nm. Only allowed level differences occur, so isolated atoms produce discrete emission lines rather than a continuum.
guided practice
4. Guided practice
Use each hint only to select the correct proportionality, amplitude rule, boundary condition or level difference.
Atomic energy levels and line spectra 19(k)–(m)
Question 1
A photon does not match any upward level difference. State the idealised absorption result.
Hint: Transitions require an allowed energy difference.
Check the model response
It is not absorbed by that isolated atom.
independent practice
5. Independent practice
Solve without repair notes and state the evidence, normalisation, quantum-number and transition assumptions.
Atomic energy levels and line spectra 19(k)–(m)
Question 1
Distinguish emission and absorption spectra and solve a generic level transition.
Check the model response
Downward transitions emit bright discrete lines; upward absorption removes matching photons from a continuum, producing dark lines. In either direction photon energy magnitude is |ΔE| = hf = hc/λ.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Atomic energy levels and line spectra 19(k)–(m)
Question 1
Levels are −6.0, −4.0 and −1.0 eV. List absorption energies from the ground state and the largest emission energy.
Check the model response
Ground-state absorption energies are 2.0 and 5.0 eV. The largest downward difference is 5.0 eV.
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Atomic energy levels and line spectra 19(k)–(m)
Question 1
Why do absorption lines align with possible emission lines for the same atom?
Check the model response
Both correspond to the same allowed energy-level differences, with opposite transition directions.