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.

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”

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 = 6.626 x 10-34 J.s

Light as a ‘Particle’ • As frequency of incident light is increased, kinetic energy of emitted e- increases linearly. F = energy needed to release e-

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.

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.

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 10-19 J Emission

Emission spectrum of H “Continuous” spectrum “Quantized” spectrum DE Any DE is possible Only certain DE are allowed

Emission spectrum of H (cont.) Light Bulb Hydrogen Lamp Quantized, not continuous

Emission spectrum of H (cont.) We can use the emission spectrum to determine the energy levels for the hydrogen atom.

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.

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 1015 1/s This suggests that the energy levels of the H atom are proportional to 1/n2

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.

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 = -2.178 x 10-18 J (!)

The Bohr Model (cont.) • Energy levels get closer together as n increases • at n = infinity, E = 0

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

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

The Bohr Model (cont.) • Example: What is the longest wavelength of light that will result in removal of the e- from H?  1

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.

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

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.