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Unformatted text preview: Solution Key for PSE#1 [1]+[2] January 29, 2007 1(a) P1.20] First we look at the energy of each photon, E photon = h = hc . Were given the wavelength, = 300 nm = 300 10 9 m . And so E photon = (6 . 626 10 34 J s )(3 10 8 m s 1 ) 300 10 9 m = 6 . 626 10 19 J photon 1 Since 6 . 626 10 19 J is delivered by each photon, we can determine how many photons were absorbed since we are told that 3 . 25 10 3 J are absorbed total. # of photons = 3 . 25 10 3 J 6 . 626 10 19 J photon 1 = 4 . 9 10 15 photons Using the equation for the photoelectric effect E photon = + 1 2 m e v 2 e (1) We can calculate the kinetic energy seeing that we know the energy of each photon and work function ( 2 . 40 eV 3 . 84 10 19 J ). KE = E photon = 6 . 626 10 19 J 3 . 84 10 19 J = 2 . 79 10 19 J Since KE = 1 2 m e v 2 e , then (remembering that 1 J = 1 kg m 2 s 2 ) v e = radicalBig 2 KE m e = radicalBig 2 2 . 79 10 19 kg m 2 s 2 9 . 11 10 31 kg = 7 . 82 10 5 m s 1 1(b) P1.4] Simply use the de Broglie equation = h p = h mv (2) Since were told that the wavelength need to be on the order of a bond length, then = 0 . 150 10 9 m , and so simply v = h m = 6 . 626 10 34 kg m 2 s 1 9 . 11 10 31 kg . 150 10 9 m = 4 . 85 10 6 m s 1 1(c) Bohr postulated that since matter has wavelike properties, if they are going to fit into an orbit, then nwavelengths must fit into a circular orbit (where n is an integer). The circumference of a circle is C = 2 r = n . Substituting equation 2, we get 2 r = n h mv , which can be rearranged to give 1 mvr = n h 2 = n planckover2pi1 (3) Since angular momentum is L = mvr = n planckover2pi1 , we can see that the quantization of hydrogen comes from the simple postulate that nwavelengths fit into a circular orbit. 1(d) Since this is a homework problem Im going to leave out most of the algebra, since thats your job....so anyway, from the homework we started with equating two forces, the coulombic force, and the force exerted on a particle moving in a loop. In this case the electron (with charge e) is moving in a loop around the nucleus (with charge +Ze)...note this is not true but this is what Bohr postulated. F coulomb = Ze 2 4 ,F loop = m v 2 r Setting these two equations equal we get Ze 2 4 = m v 2 r (4) And combining with what Bohr postulated (what you derived in 1(d)), mvr = n planckover2pi1 , we effectively have two equations and two unknowns. Equation 3 can be substituted into equation 4, and with some simple algebra, can yield r n = n 2 h 2 Ze 2 m e (5) Equation 5 can be substituted back into equation 3, and rearranging, can yield...
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 Winter '07
 Lin
 pH, Quantum Chemistry

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