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UVM PHYS 012 - Wave-Particle Duality of Light and Electrons
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Physics 012 1st Edition Lecture 33Outline of Last Lecture I. Photoelectric Effecta. Light ejects electrons from the back metal plate to create a current. Increasing voltage increases current.b. Observed Effectsi. Maximum kinetic energy of electrons is independent of light intensity.ii. Electrons are emitted instantaneously, even at lower intensity.iii. No electrons are emitted below “cutoff frequency,” regardless of intensity.1. fco = Wo/h2. Wo = work function of metal (like binding energy, varies based on material)iv. Maximum possible kinetic energy increases with increasing frequency.1. E = hf = KEmax + Wo2. hc = 1240 eV*nmIII. Compton EffectThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.a. When a photon hits a stationary electron, both the electron and the photon are scattered. The photon has a new frequency.i. hf = hf` + KEelectronii. λ + λ` = (h/mec) (1-cosθ)iii. 0° < θ < 180°iv. 0 nm < (λ – λ`) < 2h/mec nmOutline of Current Lecture IV. Compton Effecta. Photons have no mass but can impart momentum.i. Classical equation for momentum: p = mv1. Used when v << c (10% or less)ii. Relativistic equation for momentum: p = mv/√(1-[v2/c2])iii. Relativistic energy: E = mc2/√(1-[v2/c2])iv. p = Ev/c21. If v = c, then p = E/c = hf/c = h/λV. de Broglie Wavelengtha. All objects have a wavelength equal to Planck’s constant divided by the momentum of the object.i. λB = h/p = h/mvVI. Double Slit Experiment with Electronsa. We observe an interference pattern because, due to the electron’s wave characteristics, the electron reacts with both openings at once.b. Location of first minimum:i. dsinθ = λ/2ii. small angle approx. : sinθ ≈ θiii. θ = λ/2d = h/2dp1. Increased speed of electron = compressed patternVII. Heisenberg Uncertainty Principlea. When we measure an object’s position and momentum simultaneously, there are inherent uncertainties built into these measurements.i. The more accurate you measure position, the less certain you can be about momentum, and vice versa.b. The uncertainty of the position times the uncertainty of the momentum along the direction of this position is greater than or equal to one half h bar.i. ΔxΔpx ≥ ħ/2VIII. Nature of the Atoma. Plum Pudding Model: negative charges embedded in a positively-charged “pudding,” where positive charge was distributed evenly in a spherical spaceb. Ernest Rutherford Experiment: shot alpha particles (two protons, two neutrons) through a small hole in a lead screen at a thin gold leaf target surrounded by detectorsi. He found that most particles went straight through the gold but some were deflected. This meant the gold atoms were mostly empty space withtheir mass concentrated in one nuclei. The alpha particles that were deflected had been repelled by these nuclei, but the other had passed through the empty space.c. Planetary Model: electron orbits nucleusi. Problems:1. Accelerating electron must lose energy in the form of radiation, thus gradually spiraling inward until the atom collapses.2. Model doesn’t explain why only certain frequencies are emitted by atoms with


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UVM PHYS 012 - Wave-Particle Duality of Light and Electrons

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