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.
Matter-wave evidence and de Broglie wavelength 19(d)–(e)
Question 1
An electron has momentum 6.63 × 10⁻²⁴ kg m s⁻¹. Find its de Broglie wavelength and name supporting evidence.
Check the model response
λ = h/p = 1.00 × 10⁻¹⁰ m. Electron diffraction or single-electron double-slit interference supports matter-wave behaviour.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Matter-wave evidence and de Broglie wavelength 19(d)–(e)
Check this idea
Misconception: An electron is either a classical particle or a classical wave.
Repair: Quantum evidence requires a quantum state with wave-like probability behaviour and localised detections.
Check this idea
Misconception: de Broglie wavelength grows with momentum.
Repair: λ = h/p, so it decreases as momentum increases.
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.
Matter-wave evidence and de Broglie wavelength 19(d)–(e)
Model 1
Electrons accelerated through V are non-relativistic. Derive their de Broglie wavelength.
Check the model response
eV = p²/(2m), so p = √(2meV) and λ = h/√(2meV). Increasing V decreases wavelength as V⁻¹ᐟ².
guided practice
4. Guided practice
Use each hint only to select the correct proportionality, amplitude rule, boundary condition or level difference.
Matter-wave evidence and de Broglie wavelength 19(d)–(e)
Question 1
Momentum triples. State the de Broglie wavelength factor.
Hint: Use inverse proportionality.
Check the model response
λ = h/p, so wavelength becomes one third.
independent practice
5. Independent practice
Solve without repair notes and state the evidence, normalisation, quantum-number and transition assumptions.
Matter-wave evidence and de Broglie wavelength 19(d)–(e)
Question 1
Explain electron diffraction and single-particle double-slit evidence, and calculate wavelength from a stated momentum.
Check the model response
A diffraction pattern and the gradual build-up of double-slit fringes from localised detections require wave-like probability amplitudes. Use λ = h/p with SI momentum; the evidence does not mean an electron is a classical material wave.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Matter-wave evidence and de Broglie wavelength 19(d)–(e)
Question 1
A non-relativistic electron has kinetic energy 2.40 × 10⁻¹⁷ J. Find p and λ.
Check the model response
p = √(2mK) = 6.61 × 10⁻²⁴ kg m s⁻¹ and λ = h/p = 1.00 × 10⁻¹⁰ m.
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.
Matter-wave evidence and de Broglie wavelength 19(d)–(e)
Question 1
State the observation when electrons pass through a crystal with spacing comparable to λ.
Check the model response
A diffraction pattern is observed, supporting their wave nature.