Presentation on theme: "Lecture 15: Bohr Model of the Atom"— Presentation transcript:
1 Lecture 15: Bohr Model of the Atom Reading: Zumdahl 12.3, 12.4OutlineEmission spectrum of atomic hydrogen.The Bohr model.Extension to higher atomic number.
2 Light as Quantized Energy Comparison of experiment to the “classical” prediction:Classical prediction isfor significantly higherintensity as smallerwavelengths than whatis observed.“The Ultraviolet Catastrophe”
3 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 = nhnfrequencyEnergy Changen = 1, 2, 3 (integers)h = Planck’s constant = x J.s
4 Light as a ‘Particle’ • As frequency of incident light is increased, kinetic energy of emitted e-increases linearly.F = energy needed to release e-
5 Interference of Light• Shine light through a crystal and look at patternof scattering.• Diffraction can only be explained by treating lightas a wave instead of a particle.
6 Particles as waves• Electrons shine through a crystal and look at patternof scattering.• Diffraction can only be explained by treating electronsas a wave instead of a particle.
7 Photon EmissionRelaxation from one energy level to another by emitting a photon.With DE = hc/lIf l = 440 nm,DE = 4.5 x JEmission
8 Emission spectrum of H “Continuous” spectrum “Quantized” spectrum DE Any DE ispossibleOnly certain DE areallowed
9 Emission spectrum of H (cont.) Light BulbHydrogen LampQuantized, not continuous
10 Emission spectrum of H (cont.) We can use the emission spectrum to determine theenergy levels for the hydrogen atom.
11 Balmer ModelJoseph 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.
12 Rydberg ModelJohann 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 /sThis suggests that the energy levels of the H atom are proportional to 1/n2
13 The Bohr ModelNiels 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.
14 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 (!)
15 The Bohr Model (cont.) • Energy levels get closer together as n increases• at n = infinity, E = 0
16 The Bohr Model (cont.)• We can use the Bohr model to predict what DE isfor any two energy levels
17 The Bohr Model (cont.)• Example: At what wavelength will emission fromn = 4 to n = 1 for the H atom be observed?14
18 The Bohr Model (cont.)• Example: What is the longest wavelength of light that will result in removal of the e- from H?1
19 Extension to Higher Z• The Bohr model can be extended to any single electron system….must keep track of Z (atomic number).Z = atomic numbern = integer (1, 2, ….)• Examples: He+ (Z = 2), Li+2 (Z = 3), etc.
20 Extension to Higher Z (cont.) • Example: At what wavelength will emission fromn = 4 to n = 1 for the He+ atom be observed?214
21 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.