# 7 - ECE331_Lu Quantum Mechanics Three Principles 1 Energy...

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1 Lu ECE331_Lu Quantum Mechanics Three Principles: 1. Energy Quanta 2. Wave-Particle Duality 3. Uncertainty Principle Lu ECE331_Lu Energy Quanta - Discrete packets of energy. The energy of these quanta is given by E = h ν , where ν is the frequency of the radiation. All substances at finite temperatures radiate electromagnetic waves. Isolated atoms, e.g. in a gas, emit discrete frequencies, e.g. atomic spectra. Energy Quanta

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2 Lu ECE331_Lu For electromagnetic radiation, e.g. light, these particle-like discrete packets of energy are called photons . For acoustic waves, e.g. sound, these discrete packets of energy are called phonons . Each such particle has energy Photons and Phonons ϖ πν π ν h = = = 2 2 h h E Lu ECE331_Lu Photoelectric Effect
3 Lu ECE331_Lu A photon with sufficient energy can knock an electron from the surface of material. The minimum energy required to remove an electron is called the work function of the material. The maximum kinetic energy of photonelectrons is E m = h ν -q Φ , which is NOT dependent on intensity of light. Photoelectric Effect Lu ECE331_Lu The de Broglie hypothesis Since electromagnetic waves exhibit particle-like behavior, then particles should be expected to show wave-like properties. 1. The momentum of a photon (p) p = h/ λ = ħ (2 π / λ ) = ħ k λ is wavelength, k wave number, ħ modified Plank’s constant (h = 2 π ħ ).

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4 Lu ECE331_Lu 2. The de Broglie wavelength of a particle ( λ ) λ = h/p = h/(mv) , m is particle mass, v velocity. 3. Visible light spectrum: 0.39 μ m ~ 0.77 μ m Lu ECE331_Lu Davisson-Germer Experiment: the wave nature of electrons The angular distribution is very similar to an interference pattern produced by light diffracted from a grating.
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7 - ECE331_Lu Quantum Mechanics Three Principles 1 Energy...

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