OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
Wave–particle duality: (c) the de Broglie equation λ = h/p.
The de Broglie equation λ = h/p relates the wavelength λ of a particle to its momentum p, where h is the Planck constant.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 3 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
The de Broglie equation λ = h/p relates the wavelength λ of a particle to its momentum p, where h is the Planck constant. Momentum p is the product of mass and velocity, p = mv, so for a non-relativistic electron λ = h/(mv). The equation applies to all particles and provides the link between wave and particle behaviour. For an electron accelerated through a potential difference V, the kinetic energy gained is eV, so p = √(2meV) and λ = h/√(2meV). This shows that increasing the accelerating voltage decreases the wavelength. The equation is used to explain electron diffraction patterns and to calculate the wavelength of particles in wave–particle duality experiments.
What earns the marks
- The de Broglie equation is λ = h/p, where λ is the wavelength, h is the Planck constant, and p is the momentum of the particle.
- Momentum p is defined as p = mv for a particle of mass m moving at velocity v.
- For an electron accelerated through a potential difference V, the kinetic energy gained is eV, giving momentum p = √(2meV) and wavelength λ = h/√(2meV).
- The equation applies to all particles, not just electrons, and links the wave and particle properties of matter.
- Increasing the momentum of a particle decreases its de Broglie wavelength.
Common mistakes and how to put them right
Confusing the de Broglie equation with the photon energy equation E = hf.
Put it right: λ = h/p relates wavelength to momentum for matter, while E = hf relates photon energy to frequency.
Using the symbol p for power or pressure instead of momentum.
Put it right: In this context p represents momentum.
Forgetting to convert the accelerating voltage to the correct units or to use the electron charge in calculations.
Put it right: Use V in volts and e = 1.60 × 10⁻¹⁹ C, and check that the calculated wavelength is in metres.
Assuming the equation only applies to electrons.
Put it right: The de Broglie equation applies to all particles, including protons, neutrons, and atoms.
Exam tips
- Write the equation as λ = h/p and define each symbol clearly before substituting values.
- When calculating the wavelength of an accelerated electron, derive p from the kinetic energy eV and show your working.
- Check that your final wavelength is in metres and is of a sensible order of magnitude for the particle and energy involved.
Try the lesson
The start of the Wave–particle duality: (c) the de Broglie equation λ = h/p. lesson, made from checked teaching notes for this specification point.
Listen
The de Broglie equation λ = h/p relates the wavelength λ of a particle to its momentum p, where h is the Planck constant. Momentum p is the product of mass and velocity, p = mv, so for a non-relativistic electron λ = h/(mv). The equation applies to all particles and provides the link between wave and particle behaviour. For an electron accelerated through a potential difference V, the kinetic energy gained is eV, so p = √(2meV) and λ = h/√(2meV). This shows that increasing the accelerating voltage decreases the wavelength. The equation is used to explain electron diffraction patterns and to calculate the wavelength of particles in wave–particle duality experiments. A strong answer earns marks for these points. The de Broglie equation is λ = h/p, where λ is the wavelength, h is the Planck constant, and p is the momentum of the particle. Momentum p is defined as p = mv for a particle of mass m moving at velocity v. For an electron accelerated through a potential difference V, the kinetic energy gained is eV, giving momentum p = √(2meV) and wavelength λ = h/√(2meV). The equation applies to all particles, not just electrons, and links the wave and particle properties of matter. A common slip: Confusing the de Broglie equation with the photon energy equation E = hf. Instead, λ = h/p relates wavelength to momentum for matter, while E = hf relates photon energy to frequency. Exam tip: Write the equation as λ = h/p and define each symbol clearly before substituting values.
Key words
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De Broglie wavelength
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Momentum
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Wave–particle duality
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Planck constant
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See every definition
- De Broglie wavelength
- The wavelength λ of a particle, given by the equation λ = h/p.
- Momentum
- The product of mass and velocity, p = mv, for a particle of mass m moving at velocity v.
- Wave–particle duality
- The link between wave and particle behaviour of matter, explained by the de Broglie equation.
- Planck constant
- The quantity h in the de Broglie equation λ = h/p.
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