Overview
This lecture explains De Broglie theory, focusing on the wave-particle duality of matter, the mathematical derivation of the De Broglie wavelength, and key experimental evidence.
De Broglie Theory & Wave-Particle Duality
- De Broglie proposed in 1924 that particles (e.g., electrons, protons) behave both as material particles and as waves.
- This dual nature is called "wave-particle duality".
- The theory applies to all small, moving particles such as electrons, protons, and neutrons.
Derivation of the De Broglie Equation
- De Broglie used Planck’s quantum theory (E = hν) and Einstein’s mass-energy relationship (E = mc²).
- Setting E = hν and E = mc² equal gives mc² = hν.
- Since ν = c/λ, substitute to get mc² = h(c/λ).
- Rearranging leads to mc = h/λ, then λ = h/(mc).
- For any particle, λ (wavelength) = h/(mv), where m is mass and v is velocity (momentum, p = mv).
Experimental Proof of Dual Nature
- Davison and Germer (1927) diffracted electrons from a nickel crystal, confirming electron wave nature.
- Thomson and Reid (1928) diffracted high-speed electrons through thin metallic films, extending the proof.
- Both experiments used methods similar to X-ray crystallography.
Properties of Matter Waves (Wave-Matter)
- Small particles have mass and exhibit matter-like properties.
- Particles with wave nature possess wavelength, amplitude, and frequency like other waves.
- When moving, electrons, protons, and neutrons show both matter-like and wave-like properties.
Common Exam Questions
- What is De Broglie theory?
- State and derive the De Broglie equation.
- List three properties of matter waves.
- Write the mathematical derivation for the De Broglie wavelength.
Key Terms & Definitions
- Wave-particle duality — the concept that particles exhibit both wave and particle properties.
- De Broglie wavelength (λ) — the wavelength associated with a moving particle, λ = h/(mv).
- Planck’s constant (h) — a fundamental constant used in quantum mechanics.
Action Items / Next Steps
- Review and memorize the De Broglie equation and derivation.
- Prepare answers to common exam questions on De Broglie theory.
- Download the provided PDF notes for additional exam preparation.