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.
Photon evidence, energy and momentum 19(a)–(c)
Question 1
Light below a metal's threshold frequency is made more intense. Explain why no electrons are emitted and name evidence for light's wave nature.
Check the model response
Each photon still has energy hf below that required; intensity raises photon number, not energy per photon. Interference and diffraction support the wave nature of electromagnetic radiation.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Photon evidence, energy and momentum 19(a)–(c)
Check this idea
Misconception: Greater intensity raises each photon's energy.
Repair: At fixed frequency, E = hf is unchanged; intensity raises photon arrival rate.
Check this idea
Misconception: A massless photon has no momentum.
Repair: Photon momentum is p = E/c = h/λ despite zero rest mass.
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.
Photon evidence, energy and momentum 19(a)–(c)
Model 1
A photon has λ = 500 nm. Find its energy and momentum.
Check the model response
E = hc/λ = 3.98 × 10⁻¹⁹ J and p = h/λ = E/c = 1.33 × 10⁻²⁷ kg m s⁻¹. A photon is massless but has momentum.
guided practice
4. Guided practice
Use each hint only to select the correct proportionality, amplitude rule, boundary condition or level difference.
Photon evidence, energy and momentum 19(a)–(c)
Question 1
Frequency doubles. State photon energy and momentum factors.
Hint: Keep intensity separate from frequency.
Check the model response
Both E = hf and p = hf/c double.
independent practice
5. Independent practice
Solve without repair notes and state the evidence, normalisation, quantum-number and transition assumptions.
Photon evidence, energy and momentum 19(a)–(c)
Question 1
Build one evidence argument distinguishing particle and wave behaviour of electromagnetic radiation, then state photon energy and momentum relations.
Check the model response
Threshold frequency supports energy transfer in photons: below threshold no photon has enough energy, regardless of intensity. Interference and diffraction support wave behaviour. E = hf, p = E/c = h/λ; zero rest mass does not mean zero momentum.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Photon evidence, energy and momentum 19(a)–(c)
Question 1
A photon has energy 3.20 × 10⁻¹⁹ J. Find frequency and momentum, then state why threshold frequency is particle evidence.
Check the model response
f = E/h = 4.83 × 10¹⁴ Hz and p = E/c = 1.07 × 10⁻²⁷ kg m s⁻¹. A single photon below threshold cannot supply the required quantum even when more such photons arrive.
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.
Photon evidence, energy and momentum 19(a)–(c)
Question 1
A photon's wavelength halves. State energy and momentum factors.
Check the model response
Both double because E = hc/λ and p = h/λ.