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A-Level The particle nature of light, the wave nature of matter and energy quantisation
What the A-Level syllabus expects for The particle nature of light, the wave nature of matter and energy quantisation, and how to practise it.
What the syllabus expects
- Understand that a photoelectric threshold frequency argues for light behaving as particles, while interference and diffraction argue for its wave behaviour
- State that a photon is a single quantum of electromagnetic radiation and apply E = hf for its energy in problems
Scope: h is the Planck constant - Recognise that a photon, though it carries no mass, still has momentum p = E/c and p = h/λ
Scope: here c denotes light's speed in a vacuum - Understand that electron diffraction and single-particle double-slit interference back the claim that particles possess a wave nature
- Apply λ = h/p, the de Broglie wavelength, in problems
- Understand that a wavefunction ψ can stand for a particle's state, as with an atom's electron cloud, and that the squared amplitude |ψ|² gives the probability density
Scope: includes finding normalisation factors for square and sinusoidal wavefunctions - Understand that superposition holds for the wavefunctions describing a particle's position, yielding standing-wave states for a boxed particle and effects like single-particle double-slit interference
- Understand that pinning a particle down in space forces a range of momenta upon it, as the Heisenberg uncertainty principle ∆x∆p ≳ h expresses, and use this in problems
- Understand the standing-wave wavefunctions ψn that describe a particle confined to an infinite square well in one dimension
- Use En = n²h²/(8mL²) for the permitted energy levels of a mass-m particle in a one-dimensional infinite well of width L
- Understand that an electron's wavefunction in a lone atom, such as atomic hydrogen, carries separate energy levels, and reason out how these give rise to spectral lines
- Tell emission line spectra apart from absorption line spectra
- Work through problems in which a photon is taken in or given off as an atom jumps between energy levels
How it's examined
About 8% of the past-paper style questions in Rae's bank for this subject sit in this topic.
Worked examples
Example 1 (2 marks)
An atom of mass m recoils with kinetic energy K when it emits a photon of energy E. When K/E << 1, the atom's recoil can be neglected during emission. Working in terms of m and λ, give and justify two conditions under which the recoil of the atom is negligible.
Show the worked answer
By conservation of momentum the atom recoils with momentum equal to the photon momentum p = E/c = h/lambda. Recoil kinetic energy K = p²/(2m) = h²/(2 m lambda²). Photon energy E = hc/lambda. So K/E = [h²/(2 m lambda²)] / [hc/lambda] = h/(2 m c lambda). Recoil is negligible when K/E << 1, i.e. h/(2 m c lambda) << 1. This fraction is small when: (1) the atom's mass m is large (K/E is inversely proportional to m), and (2) the wavelength lambda is large, i.e. a low-energy photon (K/E is inversely proportional to lambda).
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