Lecture 15: Bohr Model of the Atom

1. 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.

2. 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”

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 = nhn frequency Energy Change n = 1, 2, 3 (integers) h = Planck’s constant = 6.626 x 10-34 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 pattern of scattering. • Diffraction can only be explained by treating light as a wave instead of a particle.

6. 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.

7. 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

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

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

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

11. 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.

12. 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

13. 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.

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 = -2.178 x 10-18 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 is for any two energy levels

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

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

20. 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

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.