Cornell Notes — Subtopic: de Broglie Wavelength & Davisson-Germer — Notes

Cue / Question	Notes
de Broglie relation	λ = h/p = h/(mv). Valid for ALL particles (electrons, protons, alpha, neutrons, even macroscopic objects)
Why macroscopic objects show no wave behavior	Very large mass → extremely small λ (immeasurably small). A cricket ball at 30 m/s: λ ≈ 10^{-34} m — undetectable.
λ for electron through V volts	KE = eV = ½ $mv^{2}$ → p = $\sqrt{2meV}$ → λ = h/ $\sqrt{2meV}$ = 1.227/√V nm
λ from kinetic energy KE	λ = h/ $\sqrt{2m·KE}$ . Apply to ANY particle given KE.
Thermal de Broglie wavelength	λ = h/ $\sqrt{3mkT}$ . k = $1.38 \times 10^{-23}$ J/K. Applies to gas molecules at temperature T.
Davisson-Germer setup	Electrons fired at Ni crystal at room temperature; detector measured intensity vs scattering angle.
Key observation	Maximum intensity at θ = 50° for V = 54 V. Predicted λ from de Broglie = 0.167 nm; experimental diffraction gave 0.165 nm. ✓
What it proved	Electrons (matter particles) exhibit wave diffraction — direct evidence of wave-particle duality of matter.
Ratio λ_e/λ_p at same V	$\sqrt{m_p/m_e}$ = $\sqrt{1836}$ ≈ 42.8. Electron wavelength ≈ 43× longer than proton at same accelerating potential.
Ratio λ_e/λ_α at same V	α-particle has charge 2e and mass 4m_p. λ_α = h/ $\sqrt{2·4m_p·2eV}$ = h/ $\sqrt{16m_p·eV}$ . λ_e/λ_α = $\sqrt{8m_p/m_e}$ ≈ $\sqrt{8×1836}$ ≈ 121.

Summary

de Broglie's hypothesis extends wave-particle duality to matter: every particle has an associated wavelength λ = h/mv. The key formula for NEET is λ = 1.227/√V nm for electrons accelerated through potential V. At the same V, heavier particles have shorter wavelength (λ ∝ 1/√m). The Davisson-Germer experiment (1927) confirmed this by observing diffraction of electrons from a Ni crystal, with the measured diffraction peak angle matching the de Broglie prediction to within 1%.$