De Broglie Wavelength Calculator
Calculate the matter wave wavelength of particles using de Broglie's equation
Calculate De Broglie Wavelength
Mass: 9.109e-31 kg
Velocity in m/s: 0.000e+0
De Broglie Wavelength Results
Formula used: λ = h / p = h / (m × v)
Planck constant: h = 6.626e-34 J⋅s
Calculated momentum: p = 0.000e+0 kg⋅m/s
Analysis
Example Calculation
Electron at 1% Speed of Light
Particle: Electron (e⁻)
Mass: me = 9.109 × 10⁻³¹ kg
Velocity: v = 0.01c = 2.998 × 10⁶ m/s
Momentum: p = mv = 2.731 × 10⁻²⁴ kg⋅m/s
Calculation
λ = h / p
λ = 6.626 × 10⁻³⁴ / 2.731 × 10⁻²⁴
λ = 2.426 × 10⁻¹⁰ m = 0.24 nm
Common Particle Masses
Units:
• 1 me = 9.109 × 10⁻³¹ kg
• 1 u = 1.661 × 10⁻²⁷ kg
Wave-Particle Duality
Matter exhibits both wave and particle properties
Smaller particles have longer wavelengths
Higher velocities give shorter wavelengths
Observable in electron microscopy
Physics Notes
Use relativistic momentum for high velocities (v > 0.1c)
Photons have λ = c/f despite zero rest mass
Wavelength becomes significant for small particles
Applications in electron diffraction and microscopy
Understanding De Broglie Wavelength
What is De Broglie Wavelength?
The de Broglie wavelength represents the wavelength associated with any moving particle with momentum. Proposed by Louis de Broglie in 1924, this concept bridges the gap between classical and quantum mechanics by showing that matter exhibits wave-like properties.
Physical Significance
- •Explains electron diffraction in crystals
- •Foundation for electron microscopy
- •Basis for quantum mechanical wave functions
- •Demonstrates wave-particle duality
De Broglie Equation
λ = h / p = h / (mv)
- λ: de Broglie wavelength (m)
- h: Planck constant (6.626 × 10⁻³⁴ J⋅s)
- p: momentum (kg⋅m/s)
- m: mass (kg)
- v: velocity (m/s)
Relativistic case: For high velocities, use p = γmv where γ = 1/√(1-v²/c²)
Applications and Examples
Electron Microscopy
Electrons with λ ≈ 0.1 nm provide resolution far superior to visible light microscopes, enabling observation of atomic structures.
Neutron Diffraction
Thermal neutrons (λ ≈ 1-2 Å) are used to study crystal structures and magnetic properties of materials.
Quantum Tunneling
Particle wavelengths determine tunneling probabilities through potential barriers, crucial in electronics and nuclear physics.