de Broglie relation
The mathematical relationship between the wavelength and momentum of a material particle.
What is de Broglie relation?
The hypothesis that all matter exhibits wave-like properties, with an associated wavelength inversely proportional to its momentum.
Key formula / rule: De Broglie Wavelength
Key points
- Understand the concept of matter waves.
- Derive and apply the de Broglie relation.
- Explain the significance of de Broglie wavelength for microscopic and macroscopic particles.
Common exam trap
Confusing the de Broglie wavelength with electromagnetic wavelengths.
Definitions
- Term
De Broglie Relation
- Meaning
The hypothesis that all matter exhibits wave-like properties, with an associated wavelength inversely proportional to its momentum.
- Term
Matter Waves
- Meaning
Waves associated with moving particles, exhibiting wave characteristics such as diffraction and interference.
- Term
Momentum
- Meaning
The product of an object's mass and its velocity; a measure of its motion.
- Term
Planck's Constant (h)
- Meaning
A fundamental physical constant that relates the energy of a photon to its frequency (E=hν) and is central to quantum mechanics.
Learning objectives
Understand the concept of matter waves.
Derive and apply the de Broglie relation.
Explain the significance of de Broglie wavelength for microscopic and macroscopic particles.
Formulae
- Name
De Broglie Wavelength
- Note
λ is the de Broglie wavelength, h is Planck's constant, and p is the momentum of the particle.
- Expression
λ = h/p
- Name
Momentum
- Note
m is the mass and v is the velocity of the particle.
- Expression
p = mv
- Name
De Broglie Wavelength (in terms of mass and velocity)
- Note
Combines the above two formulas.
- Expression
λ = h/mv
- Name
De Broglie Wavelength (in terms of kinetic energy)
- Note
Ek is the kinetic energy of the particle. Derived from p = √(2mEk).
- Expression
λ = h / √(2mEk)
- Name
De Broglie Wavelength (for charged particle)
- Note
q is the charge, V is the accelerating potential difference. Derived from Ek = qV.
- Expression
λ = h / √(2mqV)
Prerequisites
Basic understanding of momentum.
Knowledge of Planck's constant.
Concept of wave-particle duality of light.
Common mistakes
Confusing the de Broglie wavelength with electromagnetic wavelengths.
Forgetting to use consistent units (SI units are preferred).
Assuming the relation applies only to microscopic particles without understanding why it's negligible for macroscopic ones.
Keywords
De Broglie
Matter waves
Wave-particle duality
Momentum
Planck's constant
Wavelength
Quantum mechanics
Practice preview
The de Broglie wavelength of an electron accelerated through a potential difference V is proportional to:…
medium
According to the de Broglie relation, the wavelength of a particle is inversely proportional to its:…
easy
A particle of mass m and momentum p has a de Broglie wavelength λ. If its momentum is increased to 2p, what will be its new de Broglie wavelength?…
easy