Physics 012 1st Edition Lecture 34Outline of Last Lecture I. 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/λII. 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/mvIII. 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 patternIV. Heisenberg Uncertainty Principlea. When we measure an object’s position and momentum simultaneously, there are inherent uncertainties built into these measurements.These 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.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/2V. 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 excitation.Outline of Current Lecture VI. When an electron goes from a higher (ni) to lower (nf) energy state, light of wavelength λis emitted.a. 1/λ = R(1/nf2 – 1/ni2)i. R = Rydberg constant = 1.097 x 107 m-1b. Balmer series: series of wavelengths emitted by hydrogen within the visible spectrum, where nf = 2.VII. Bohr modified planetary modela. Electrons do not continuously emit radiation.b. We have “stationary states.”c. Radiation is emitted by electrons when moving to a smaller orbit (lower energy).d. Energy emitted by electron = Ei – Ef = hf = hc/λe. Angular momentum is also quantized: L = nħ = rmevVIII. Energy Level Diagram for
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