Physics Exam Review: Thermal Radiation, Photoelectric Effect, Matter Waves - Prof. Brian L, Exams of Physics

Download Physics Exam Review: Thermal Radiation, Photoelectric Effect, Matter Waves - Prof. Brian L and more Exams Physics in PDF only on Docsity! Exam 1 Review You are responsible (i.e., put them on your cheat sheet) for knowing constants like Boltzmann’s constant, c, ℏ, etc. You are responsible for understanding what all of the equations mean and how they are derived. I do not guarantee that these equations are all exactly correct! Chapter 1 Thermal Radiation and Plank’s law What about thermal radiation cannot be explained by classical electromagnetism? Why? ρ(ν)=8πν2kT/c3 Rayleigh-Jean’s formula Plank’s postulate: ΔE=hν / ( ) 1h kTe h E      Plank’s blackbody spectrum: 2 3 / 8 ( ) 1h kT h c e        Stefan-Boltzmann Law: R=ς T4 Wien displacement Law: λmaxT=2.9 mm K Chapter 2 Photoelectric Effect What about the photoelectric effect cannot be explained by classical electromagnetism and mechanics? Why? Einstein’s theory of the photoelectric effect: E=hν KEmax=hν-w0 Compton Effect What about the photoelectric effect cannot be explained by classical electromagnetism and mechanics? Why? Δλ=λC(1-cosθ) Chapter 3 Matter waves deBroglie’s hypothesis: λ=h/p What about the Davisson-Germer experiments cannot be explained using classical mechanics? Why? Bragg reflection from a crystal: nλ=2 d sin ϕ The “wave-particle duality”; correspondence between intensity in a light field and the wavefunction Born’s interpretation of the wavefunction: P(x,t) dx =|Ψ(x,t)|2 dx The uncertainty principle, Bohr’s microscope thought experiment: ΔpΔx≥ℏ/2 ΔEΔt≥ℏ/2 Superposition of waves and the uncertainty principle, phase velocity vs. group velocity: vg=dω/dk Chapter 4 Thomson’s model   2 2/ 2 2I eN       Rutherford’s model What about Rutherford’s experiments could not be explained by Thomson’s model? Why? 2 2 4 2 0 2 1 2 sin( ) ( ) 4 /2 sin ( 2) zZe I Mv t N                   Bohr’s model L=nℏ ν=(Ei-Ef)/h 2 2 0 2 4 n r mZe      2 4 2 22 0 1 4 2 mZ e E n    deBroglie’s interpretation in terms of standing electron waves Chapter 5 Schrödinger’s theory TDSE: 22 2 ( , ( , ) ( , ) ( , )) 2 x t x t xV x t m x t t i            TISE: 2 2 2 ( , ) (( ) ) ( ) 2 V x m x x t x E x          /( , ) ( ) iEtx t x e  