Core Idea: Matter (particles) has wave-like properties. This is wave-particle duality.
Key Equation: λ = h / (mv) or λ = h / p (where p = mv = momentum)
- λ = de Broglie wavelength (m)
- h = Planck’s constant (6.626 x 10⁻³⁴ J s)
- m = mass (kg)
- v = velocity (m/s)
- p = momentum (kg m/s)
Meaning: A moving particle has an associated wavelength. Higher momentum (mass or velocity) means shorter wavelength.
Significance
- Microscopic world: Crucial for understanding electrons, atoms, etc. Explains electron diffraction (evidence for wave nature).
- Macroscopic world: Applies to all objects, but the wavelength is so tiny we don’t notice it.
Example Calculation
Calculate the de Broglie wavelength of an electron (m = 9.11 x 10⁻³¹ kg) moving at 1.0 x 10⁶ m/s.
λ = h / (mv) λ = (6.626 x 10⁻³⁴ J s) / ((9.11 x 10⁻³¹ kg) * (1.0 x 10⁶ m/s)) λ ≈ 7.27 x 10⁻¹⁰ m
