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**Lecture 15: 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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**Light as Quantized Energy**

Comparison of experiment to the “classical” prediction: Classical prediction is for significantly higher intensity as smaller wavelengths than what is observed. “The Ultraviolet Catastrophe”

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**Light as Quantized Energy**

Planck found that in order to model this behavior, one has to envision that energy (in the form of light) is lost in integer values according to: DE = nhn frequency Energy Change n = 1, 2, 3 (integers) h = Planck’s constant = x J.s

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**Light as a ‘Particle’ • As frequency of incident light is increased,**

kinetic energy of emitted e- increases linearly. F = energy needed to release e-

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Interference of Light • Shine light through a crystal and look at pattern of scattering. • Diffraction can only be explained by treating light as a wave instead of a particle.

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Particles as waves • Electrons shine through a crystal and look at pattern of scattering. • Diffraction can only be explained by treating electrons as a wave instead of a particle.

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Photon Emission Relaxation from one energy level to another by emitting a photon. With DE = hc/l If l = 440 nm, DE = 4.5 x J Emission

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**Emission spectrum of H “Continuous” spectrum “Quantized” spectrum DE**

Any DE is possible Only certain DE are allowed

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**Emission spectrum of H (cont.)**

Light Bulb Hydrogen Lamp Quantized, not continuous

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**Emission spectrum of H (cont.)**

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 in the H atom spectrum could be reproduced by: 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: n1 = 1, 2, 3, ….. n2 = n1+1, n1+2, … Ry = 3.29 x /s This suggests that the energy levels of the H atom are proportional to 1/n2

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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.

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The Bohr Model (cont.) Bohr model for the H atom is capable of reproducing the energy levels given by the empirical formulas of Balmer and Rydberg. Z = atomic number (1 for H) n = integer (1, 2, ….) • Ry x h = x J (!)

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**The Bohr Model (cont.) • Energy levels get closer together**

as n increases • at n = infinity, E = 0

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The Bohr Model (cont.) • We can use the Bohr model to predict what DE is for any two energy levels

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The Bohr Model (cont.) • Example: At what wavelength will emission from n = 4 to n = 1 for the H atom be observed? 1 4

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The Bohr Model (cont.) • 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 (atomic number). Z = atomic number n = integer (1, 2, ….) • Examples: He+ (Z = 2), Li+2 (Z = 3), etc.

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**Extension to Higher Z (cont.)**

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

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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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