Short on time? This page is the recap. For explanations, Figure 1 and the worked examples, use the full study guide.
Recap
- Quantum theory was developed because classical physics could not explain atomic spectra, blackbody radiation or the photoelectric effect. It is needed at atomic and subatomic scales.
- Light can be modelled as a wave and as a stream of photons. A photon is massless, neutral and has energy proportional to its frequency.
- Photons travel in straight lines unless they interact with matter. In a vacuum all photons travel at c; in a medium, at c/n.
- Wave-particle duality: in a dim two-slit experiment, each photon or electron arrives as one dot, but many dots build up an interference pattern.
- Every particle has a de Broglie wavelength. Wave effects show up only when λ is comparable to the size of the system.
- In a bound system (such as an electron in an atom), energy and momentum are quantized: only certain values are allowed.
Key relationships
| Relationship | Symbols and units | Use it to |
|---|---|---|
| E = hf = hc/λ | h = 6.63 × 10⁻³⁴ J·s = 4.14 × 10⁻¹⁵ eV·s; λ is the vacuum wavelength | find the energy of one photon |
| 1 eV = 1.60 × 10⁻¹⁹ J | switch between eV and J | |
| N/t = P/E | P in W, E in J | count photons per second in a beam |
| v = c/n, λ_medium = λ/n | f and E unchanged | describe light in a medium |
| λ = h/p = h/(mv) | p in kg·m/s, λ in m | find a particle’s de Broglie wavelength |
| λ = h/√(2mqΔV) | particle accelerated from rest through ΔV | link wavelength to accelerating voltage |
Functional dependence to remember: E ∝ f ∝ 1/λ for photons; λ ∝ 1/p for particles; λ ∝ 1/√ΔV for a particle accelerated from rest.
Assumptions behind the numbers
- Speeds are much less than c, so p = mv and K = ½mv² (check v/c if unsure).
- Particles start from rest when accelerated through ΔV.
- Wavelengths in E = hc/λ are vacuum wavelengths.
Mistakes to avoid
- Thinking intensity sets photon energy. Frequency sets it; intensity sets the number of photons.
- Giving photons mass or charge.
- Using the in-medium wavelength in E = hc/λ. Frequency, and so photon energy, does not change in a medium.
- Inverting the de Broglie relation. Heavier or faster means shorter λ.
- Mixing eV and J. Convert before using h in J·s.
- Saying an electron moves along a wavy path. The wave describes where it is likely to be detected.
Quick self-check
- What is the energy of a 620 nm photon, in eV? (3.21 × 10⁻¹⁹ J, which is 2.01 eV)
- Find the de Broglie wavelength of an electron moving at 2.0 × 10⁶ m/s. (3.6 × 10⁻¹⁰ m)
- A particle’s momentum doubles. What happens to its de Broglie wavelength? (It halves.)
Next: practice questions.