De Broglie hypothesis

📋 Teacher notes

• •De Broglie (1924): if light waves can behave as particles (photons), then particles should behave as waves — λ = h/mv. Confirmed by Davisson–Germer electron diffraction in 1927.
• •The key comparison: an electron at 2×10⁶ m/s has λ ≈ 0.36 nm (atom-sized → diffracts off crystals) while a cricket ball has λ ≈ 10⁻³⁴ m — unimaginably smaller than a nucleus, so we never see cricket balls diffract.
• •Larger momentum → shorter wavelength. Switch particles and watch λ collapse: mass in the denominator is why wave behaviour is invisible for everyday objects.
• •Electron microscopes exploit this: electrons accelerated through kilovolts get λ far below visible light (400–700 nm), resolving individual atoms.
• •For an electron accelerated through voltage V: λ = h/√(2meV) ≈ 1.23/√V nm — a favourite exam derivation (KE = eV = p²/2m).