de Broglie Wavelength
λ = h/(mv) — Gaussian wavepacket across 4 particle types from electron to dust.
Key Notes
Louis de Broglie (1924): every moving particle of momentum p has an associated wave of wavelength λ = h/p.
For a particle of mass m and speed v (non-relativistic): λ = h/(mv).
For an electron accelerated through V volts: λ = h/√(2meV) = 12.27/√(V[volts]) Å.
Larger momentum (heavier or faster) ⇒ smaller wavelength.
Matter waves were experimentally verified by Davisson-Germer (electron diffraction off Ni crystal, 1927) and G.P. Thomson (electron diffraction through thin foils).
Atom-interference experiments now confirm de Broglie waves for atoms and even C₆₀ buckyballs.
de Broglie's hypothesis led directly to Schrödinger's wave equation and modern quantum mechanics.
Formulas
de Broglie wavelength
Universal — any particle, any speed (non-rel).
Electron via potential difference V
V in volts; very useful shortcut for V < 1 kV.
Through kinetic energy
K = ½mv² = eV for accelerated electrons.
Relativistic correction
Becomes important for K ≳ mc² (e.g., > 0.5 MeV for electrons).
Important Points
Smaller mass / smaller speed ⇒ LONGER wavelength ⇒ wave nature more apparent.
An electron at 100 V acceleration has λ ≈ 1.23 Å — comparable to atomic spacings ⇒ diffraction works.
A proton at 100 V has λ ≈ 0.029 Å — needs much higher KE to do crystallography.
Heat-of-Schrödinger 'matter wave' is the wavefunction ψ — its modulus squared |ψ|² is the probability density.
Useful shortcut: For electron, λ[Å] = 12.27/√V (V in volts).
Atom interferometers use cold atoms (slow) to make λ_dB ~ μm — large enough to make wave phenomena practically engineerable.
de Broglie Wavelength notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 12 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.