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The historical development of quantum mechanics through the failures of classical mechanics, focusing on the concepts of blackbody radiation, the photoelectric effect, and the de broglie relation. It covers the discoveries of max planck, albert einstein, and louis de broglie, and their impact on our understanding of the fundamental nature of energy and matter.
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2 Blackbody Radiation Blackbody: An ideal emitter of radiation capable of absorbing and emitting all frequencies of light uniformly Hot objects emit electromagnetic radiation with frequencies given by the spectral density r ( n ,T) : Failures of Classical Mechanics: Example 1 Frequency Distribution of a Blackbody:
n r n n k T d c T d B 3 2 8 ,
n r n n E d c T d osc 3 2 8 , E (^) osc kB T i. As T, maximum in r shifts to n ( l) ii. Total energy density is the area under the curve ( as T^4 ) ln c
4 The Photoelectric Effect Failures of Classical Mechanics: Example 2 Albert Einstein confirmed Max Planck’s hypothesis of the quantization of light (1905): e- e- e- h n Metal Surface
2
2
e e
Conservation of Energy: Threshold Energy (Work Function) Photon Energy Kinetic Energy of the Photoelectron: Work function (): the energy required to remove an electron from the valence level of a metal to infinity. Case 1: EF EV 2 1 KEe- h n 1 E h n 2 E
h n 1
h n 2
Energy of a photon:
5 The de Broglie Relation Failures of Classical Mechanics: Example 3 Louis de Broglie suggested that particles have a wavelength (1923):
Momentum: de Broglie Relation: Kinetic Energy in Terms of Momentum:
2 2
de Broglie Relation (in terms of mass, velocity):
7 Diffraction Experiments: Failures of Classical Mechanics: Example 3/ Wave-particle duality of matter as evidenced by diffraction: http://www.colorado.edu/physics/2000/schroedinger/two-slit2.html http://www.rpi.edu/~schubert/Educational-resources/Educational-resources.htm Double-slit diffraction of light (early 1800s):
http://www.faculty.virginia.edu/consciousness/new_page_6.htm^8 Spectroscopy: (^) Failures of Classical Mechanics: Example 5 Atomic emission spectra provide the most compelling evidence for energy quantization: continuous discrete
