Theme E — Nuclear and Quantum Physics
E.2.4 The de Broglie Wavelength — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 14 of 45 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
E.2.4 The de Broglie Wavelength — IB PHYSICS HL notes: Use λ = h/p and λ = h/√(2mEk) and describe electron diffraction as evidence for matter waves.De Broglie's idea — if waves can behave like particles, particles may behave like wavesProposed in 1924Matter wave — every moving pa…
- Definition
- What the symbols mean
- Larger momentum
- Everyday objects
- Typical metal electron
- Graphite film
Part 1 of 7The hypothesis
De Broglie's idea
- De Broglie's idea if waves can behave like particles, particles may behave like waves
- Proposed in 1924
Matter wave
- Matter wave every moving particle has an associated wave
Definition
- Definition the de Broglie wavelength is the wavelength associated with a moving particle
Equation
- λ = h/p = h/mvWhat the symbols mean: λ = de Broglie wavelength (m) · h = 6.63 × 10−34 J s · p = momentum (kg m s−1) · m = mass (kg) · v = speed (m s−1)
Part 2 of 7Kinetic energy form
Momentum
- Momentum p = √(2mEk) from Ek = p2/2m
Wavelength
- λ = h/√(2mEk)
Larger momentum
- Larger momentum a shorter wavelength
Everyday objects
- Everyday objects the wavelength is far too small for quantum effects to be observed
Part 3 of 7Electrons accelerated through a voltage
Energy
- Energy eV = ½mv2 so p = √(2meeV)
Wavelength
- λ = h/√(2meeV)
Size
- 100 V gives about 0.123 nm, similar to atomic spacing in a crystal
Typical metal electron
- Typical metal electron a de Broglie wavelength of about 10 nm
Part 4 of 7Electron diffraction
1
Condition
- Condition electrons must pass through a gap similar to their wavelength such as an atomic lattice
2
Graphite film
- Graphite film the gaps between atomic planes act like slits
3
Pattern
- Pattern a series of concentric rings, whereas particles would spread uniformly
4
Higher voltage
- Higher voltage greater speed, momentum and kinetic energy, shorter wavelength and smaller rings
5
Lower voltage
- Lower voltage larger rings
6
Maximum
- Maximum sin θ = λ/d for the first maximum with d the atomic spacing
7
First minimum
- First minimum it is at half that value and not zero
8
Evidence
- Evidence the first clear evidence that matter has wave properties
Part 5 of 7Experimental confirmation
Experimental confirmation
Davisson and Germer (1927)
- Davisson and Germer (1927) electrons on a nickel crystal gave reflected intensity peaks at specific angles like X-ray diffraction
G. P. Thomson
- G. P. Thomson electrons through a polycrystalline foil gave rings on a screen
Electron microscope
- 100 kV electrons have λ of about 4 pm and resolve far finer detail than visible light
Part 6 of 7Comparing particles
Comparing particles
Same kinetic energy
- Same kinetic energy p = √(2mEk) so the heavier particle has the shorter wavelength
Proton and electron
- Proton and electron a proton has a wavelength about 43 times smaller
Same speed
- λ ∝ 1/m
Same accelerating voltage
- λ ∝ 1/√m for equal charges
Bohr link
- Bohr link whole numbers of wavelengths around an orbit, 2πr = nλ, give mvr = nh/2π
Part 7 of 7More from the specification
More from the specification
Einstein's Photoelectric Equation
- When incident photons illuminate a metal surface, photoelectrons are emitted with maximum kinetic energy Ek,max = h f - Φ,
- where h f is the incident photon energy and Φ is the metal's work function.
Threshold Frequency and Work Function
- Photoelectric emission cannot occur unless incident radiation frequency exceeds the threshold frequency f0,
- where the minimum photon energy matches the work function (h f0 = Φ).
Photon Intensity vs. Photon Energy
- Increasing incident light intensity increases the rate of emitted photoelectrons per second,
- but does not alter their maximum kinetic energy,
- which depends strictly on radiation frequency.
De Broglie Wavelength of Matter
- Every moving particle of mass m and velocity v possesses wave properties with a de Broglie wavelength defined by λ = h / p = h / (m v).
Einstein's Photoelectric Equation
- When incident photons illuminate a metal surface, photoelectrons are emitted with maximum kinetic energy Ek,max = h f - Φ,
- where h f is the incident photon energy and Φ is the metal's work function.
Threshold Frequency and Work Function
- Photoelectric emission cannot occur unless incident radiation frequency exceeds the threshold frequency f0,
- where the minimum photon energy matches the work function (h f0 = Φ).
Photon Intensity vs. Photon Energy
- Increasing incident light intensity increases the rate of emitted photoelectrons per second,
- but does not alter their maximum kinetic energy,
- which depends strictly on radiation frequency.
De Broglie Wavelength of Matter
- Every moving particle of mass m and velocity v possesses wave properties with a de Broglie wavelength defined by λ = h / p = h / (m v).
Einstein's Photoelectric Equation
- When incident photons illuminate a metal surface, photoelectrons are emitted with maximum kinetic energy Ek,max = h f - Φ,
- where h f is the incident photon energy and Φ is the metal's work function.
Threshold Frequency and Work Function
- Photoelectric emission cannot occur unless incident radiation frequency exceeds the threshold frequency f0,
- where the minimum photon energy matches the work function (h f0 = Φ).
Photon Intensity vs. Photon Energy
- Increasing incident light intensity increases the rate of emitted photoelectrons per second,
- but does not alter their maximum kinetic energy,
- which depends strictly on radiation frequency.
De Broglie Wavelength of Matter
- Every moving particle of mass m and velocity v possesses wave properties with a de Broglie wavelength defined by λ = h / p = h / (m v).
Theory
- A well-tested, wide-ranging explanation supported by evidence.
Stopping potential
- The p.d. that stops the most energetic photoelectrons
Wave-particle duality
- The property that radiation and matter show both wave and particle behaviour.
Compton scattering
- Scattering of a photon by an outer electron, with transfer of part of the photon's energy.
Frequency
- Revolutions per second, f = 1/T.What the symbols mean: T = period, the time for one complete wave (s) · f = frequency (Hz)
Photon
- A quantum of electromagnetic energy, E = hf
Threshold
- The output value at which a switching circuit changes state.
Photoelectron
- An electron emitted from a metal surface by the photoelectric effect.
Current
- Flow of electrons in a circuit.
Radiation
- Transfer by electromagnetic waves, requiring no medium
Constant
- Not changing.
Scattering
- Deflection of particles from their original path.
E = hf
What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10−34 J s) · f = frequency (Hz)
Key terms
| Term | Meaning |
|---|---|
| de Broglie wavelength | The wavelength associated with a moving particle, λ = h/p. |
| Matter wave | The wave associated with a moving particle. |
| Electron diffraction | The diffraction of electrons by an atomic lattice that shows their wave nature. |
| Momentum | p = mv for a particle of mass m and speed v. |
Avoid these mistakes
1
Using the de Broglie equation with energy instead of momentum.
2
Forgetting the square root when finding p from accelerating voltage.
3
Saying large objects have no wavelength — it is too small to detect.
4
Assuming a larger voltage increases the wavelength — it decreases it.
5
Mixing up particle mass and charge when comparing different particles.
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