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# Chapter3_all - PHY3063 R. D. Field In Search of a Missing...

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PHY3063 R. D. Field Department of Physics Chapter3_1.doc University of Florida In Search of a Missing Fundamental Constant In the theory of relativity the constant c plays a fundamental role: β = v/c << 1 (non-relativistic “classical” physics holds) β = v/c 1 (must use relativity) Question: Does an analogous criterion exist which tells us when we must apply quantum mechanics and when the “classical” theory is okay? Answer: Yes! Planck’s constant. s eV s J h × = × = 15 34 10 136 . 4 10 626 . 6 The dimensions of Planck’s constant are [energy]×[time]= [length]×[momentum]= [angular momentum]= [ “action” ] Criterion: If for a physical system any “natural” dynamical variable which has dimensions of “action” assumes a numerical value comparable to Planck’s constant, h, then the behavior of the system must be described within the framework of Quantum Mechanics . The Discovery of Planck’s Constant Outstanding problems at the beginning of the century: (a) The problem of “black-body” radiation. (b) The problem of the photoelectric effect. (c) The problem of the stability of the size of atoms. (d) Compton scattering. The missing constant! It is small! Studying these problems led to the discovery of Planck’s constant and to the development of Quantum Mechanics!

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PHY3063 R. D. Field Department of Physics Chapter3_2.doc University of Florida Some Important Constants (in 1900) (A) The speed of light in a vacuum: s m c / 10 997925 . 2 8 × = (B) Avogadro’s number: mole N A / 10 022 . 6 23 × = N A is the number of entities in a mole of anything. A mole is the amount of any substance that contains as many entities as there atoms in 12 grams of Carbon-12 . N A is the number of Carbon-12 atoms in 12 grams of Carbon-12. Thus, ) 1 ( 12 12 AMU N g A × × = and 23 27 3 10 02 . 6 10 66 . 1 / 10 ) 1 /( 1 × × = = kg kg AMU g N A N A is the number of molecules in a mole of any gas. N A is the link between microphysics and macrophysics. It is large because atoms and molecules are small. (C) Mass of the hydrogen atom: kg M H 27 10 67 . 1 × = M H is equal to the mass of a proton, M p , to within 1 part in 2000. A mole of hydrogen molecules ( i.e. H 2 ) has a mass of 2 grams. Thus grams M N M N M N p A H A H A 2 2 2 2 = (D) The magnitude of the charge of an electron e: C e 19 10 6 . 1 × = The charge carried by a mole of singly charged ions (each with charge e) is called Faraday’s Constant F = N A e = 96,500 C . (E) The ratio of charge to mass for an electron and proton: kg C m e e / 10 76 . 1 / 11 × = kg C M e p / 10 6 . 9 / 7 × = Determined by J.J. Thomson in 1897 by bending beams of protons and electrons in a magnetic field. (F) The mass of an electron: kg m e 31 10 11 . 9 × = This was inferred from e and e/m e . Not known very well in 1900!
PHY3063 R. D. Field Department of Physics Chapter3_3.doc University of Florida Temperature and Boltzmann’s Constant What is temperature? As the temperature increases the average kinetic energy associated with the random motion of the constituents ( i.e. atoms or molecules) of the macroscopic body increases. At 0 o K all random motion stops. Note that T K = T C + 273.15 and T F = 9T C /5 + 32 , where T

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## This note was uploaded on 04/17/2008 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.

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Chapter3_all - PHY3063 R. D. Field In Search of a Missing...

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