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.

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 J Emission

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

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

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 (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.

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 /s

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.

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 = x J

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

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

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

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

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

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.