notes_Lecture_17_111210

notes_Lecture_17_111210 - Lecture 17: Quantum Mechanics...

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Unformatted text preview: Lecture 17: Quantum Mechanics Reading: Zumdahl 12.5 & 12.6 Problems for Extra Practice 47, 49 (Chapter 12) Outline Bohrs Model of the hydrogen atom (12.4) Quantum-Mechanical model of the atom (12.5) The particle in a box (12.6) The wave equation for the hydrogen atom (12.7) Emission spectrum of H We can use the emission spectrum to determine the energy levels for the hydrogen atom. The emitted photon shows up as one of the lines in the spectrum... but it represents a change between two energy levels in the atom. E = hc/ b = hc/ E If = 440 nm, = 4.5 x 10-19 J The Balmer Model Joseph Balmer (1885) first noticed that the frequency of visible lines in the H atom spectrum could be reproduced by: ... 5 , 4 , 3 1 2 1 2 2 =- n n The above equation predicts that as n increases, the frequencies become more closely spaced. Empirical!!! The Rydberg Model Johann Rydberg extends the Balmer model by finding more emission lines outside the visible region of the spectrum: - = 2 2 2 1 1 1 n n R y This suggests that the energy levels of the H atom are proportional to 1/n 2 Niels Bohr uses the emission spectrum of hydrogen to develop a quantum model for H ... 3 , 2 , 1 1 = n ... , 2 , 1 1 1 2 + + = n n n 1 15 10 29 . 3- = s R y Empirical!!! Bohrs Model of the H Atom - =- 2 2 18 J 10 178 . 2 n Z E Z = atomic number (1 for H) n = integer (1, 2, .) Energy levels get closer together as n increases. At n = infinity ( ), E = 0no interaction between nucleus and electron. Electron circles the nucleus in only certain allowed circular orbits. Orbit energies are quantized, and described according to: Identify the energy level diagram that best represents the H atom: A B C D The Bohr Model (cont.) We can use the Bohr model to predict what E is for any two energy levels (we can predict the photon ) E = E final- E initial ( ) -- - =-- 2 2 18 2 2 18 1 ) (Z J 10 178 . 2 1 ) J(Z 10 178 . 2 initial final n n - - =- 2 2 2 18 1 1 ) J(Z 10 178 . 2 initial final n n The Bohr Model (cont.) Example: At what wavelength will emission from n = 4 to n = 1 for the H atom be observed?...
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This note was uploaded on 09/29/2011 for the course CHM 101 taught by Professor Ma during the Spring '11 term at Beacon FL.

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notes_Lecture_17_111210 - Lecture 17: Quantum Mechanics...

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