HW1 solu - CHEM 442: Homework Assignment #1 Solutions...

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Spring 2010 1 History of Quantum Mechanics Name Year Topic W. Roentgen 1901 discovering Roentgen/X-rays P.Curie 1903 research on Becquerel radiation M. Curie Max Planck 1918 blackbody radiation/energy quanta N. Bohr 1922 Bohr model/structure of atoms A. Einstein 1921 photoelectric effect L. de Broglie 1929 explaining the wave nature of electrons J. Chadwick 1935 discovering the neutron G. Binnig 1986 scanning tunneling microscope H. Rohrer E. Rutherford 1908 investigations of radioactive substances K. Fukui 1981 theories of chemical reactions R. Hoffman R. Marcus 1992 theories of electron transfer reactions Table 1: Nobel Prize winners in work related to the development/advancement of the quantum theory. 2 Black Body Radiation a The Planck radiant energy density is: ρ ( ν, T ) = 8 πh c 3 ν 3 e hν/k b T - 1 (1) The exponential term in Eqn 1 can be expanded into the following Taylor series: e hν/k b T = 1 + k b T + ( hν/k b T ) 2 2! + . . . (2) For low frequencies, we can approximate the exponential function to the second term in Eqn 2. Applying this approximation to Eqn 1 gives: ρ ( ν, T ) = 8 πh c 3 ν 3 1 + k b T - 1 = 8 πν 2 k b T c 3 which is the classical Rayleigh-Jeans distribution. 1
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HW1 solu - CHEM 442: Homework Assignment #1 Solutions...

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