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Lecture 16: Bohr Model of the Atom Reading: Zumdahl 12.3, 12.4 Outline –Emission spectrum of atomic hydrogen. –The Bohr model. –Extension to higher atomic number.

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Photon Emission System drops from a higher energy level to a lower one by spontaneously emitting a photon. E = hc/ If = 440 nm, = 4.5 x 10 -19 J Emission

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“Continuous” spectrum “Quantized” spectrum Any E is possible Only certain E are ‘allowed’ transitions EE EE

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Emission spectrum of atomic H Light Bulb: Continuous spectrum Hydrogen Lamp: Discrete lines only Quantized, not continuous

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We can use the emission spectrum to determine the energy levels for the hydrogen atom.

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Balmer Model Joseph Balmer (1885) first noticed that the frequency of visible lines (transitions) in the H atom spectrum could be reproduced by a formula where frequency (v) varies according to: n = 3, 4, 5, ….. The above equation predicts that as n increases, the frequencies become more closely spaced.

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Rydberg Model Johann Rydberg extends the Balmer model by finding more emission lines outside the visible region of the spectrum (uv, ir): n 1 = 1, 2, 3, ….. This suggested that the energy levels of the H atom are proportional to 1/n 2 n 2 = n 1 +1, n 1 +2, … R y = 3.29 x 10 15 1/s

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The Bohr Model Niels Bohr uses the emission spectrum of hydrogen to develop a quantum model for H. Central idea: electron circles the “nucleus” in only certain allowed circular orbitals. Bohr postulates that there is Coulombic attraction between e- and nucleus (+). However, classical physics is unable to explain why an H atom doesn’t simply collapse, with the electron spiraling into the nucleus.

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The Bohr model for the H atom is capable of reproducing the energy levels given by the empirical formulas of Balmer and Rydberg. Z = atomic no. (1 for H) n = integer (1, 2, ….) Note: R y x h = -2.178 x 10 -18 J

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Energy levels get closer together as n increases for n = infinity, E = 0, so reference state is electron completely removed from the H atom.

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We can use the Bohr model to predict what E is for any two energy levels:

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Example: At what wavelength will emission from n = 4 to n = 1 for the H atom be observed? 14

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Example: What is the longest wavelength of light that will result in removal of the e - from H? 1

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Extension to Higher Z The Bohr model can be extended to any single electron system….must keep track of Z. Examples: He + (Z = 2), Li +2 (Z = 3), etc. Z = atomic number n = integer (1, 2, ….)

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Example: At what wavelength will emission from n = 4 to n = 1 for the He + atom be observed? 2 14 Note:

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Where does this go wrong? The Bohr model’s successes are limited: Doesn’t work for multi-electron atoms. The “electron racetrack” picture is incorrect. That said, the Bohr model was a pioneering, “quantized” picture of atomic energy levels.

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