De Broglie Wavelength Calculator

Calculate the de Broglie wavelength of particles, which describes the wave-like properties of matter as proposed by Louis de Broglie in 1924.

Calculation Method
Mass and Velocity Parameters
Momentum Parameters
Kinetic Energy Parameters
Temperature Parameters (for gases)
g/mol
Calculation Results
De Broglie Wavelength

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Frequency

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Calculation Details
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About De Broglie Wavelength
The Wave-Particle Duality

In 1924, French physicist Louis de Broglie proposed that all matter exhibits both wave-like and particle-like properties. This revolutionary concept, known as wave-particle duality, is a fundamental principle of quantum mechanics.

De Broglie Wavelength Formula

The de Broglie wavelength (λ) of a particle is related to its momentum (p) by the equation:

λ = h/p

Where:

  • λ is the wavelength (in meters)
  • h is Planck's constant (6.626 × 10-34 J·s)
  • p is the momentum of the particle (in kg·m/s)

For a particle with mass m and velocity v, the formula becomes:

λ = h/(m·v)

Applications

The de Broglie wavelength concept has numerous applications in:

  • Electron Microscopy: Electron microscopes use the wave properties of electrons to achieve much higher resolution than optical microscopes.
  • Neutron Diffraction: Used to study the structure of crystals and materials.
  • Quantum Computing: The wave nature of particles is fundamental to quantum computing principles.
  • Semiconductor Physics: Understanding electron behavior in semiconductors.
Relativistic Effects

For particles moving at speeds close to the speed of light, relativistic effects become significant. The relativistic momentum is given by:

p = γmv

Where γ is the Lorentz factor: γ = 1/√(1-(v/c)²)

Thermal De Broglie Wavelength

For gases at temperature T, the average thermal de Broglie wavelength is:

λth = h/√(2πmkT)

Where k is Boltzmann's constant (1.381 × 10-23 J/K).

Historical Significance

The de Broglie hypothesis was a pivotal development in quantum theory, helping to establish the wave-particle duality concept. It was experimentally confirmed by the Davisson-Germer experiment in 1927, which demonstrated electron diffraction, confirming the wave-like properties of electrons.