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 3 Emission spectrum of H
DE DE Any DE is possible Only certain DE are allowed 4 Emission spectrum of H (cont.) Light Bulb Hydrogen Lamp Quantized not continuous 5 Emission spectrum of H (cont.) We can use the emission spectrum to determine the energy levels for the hydrogen atom. 6 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.
7 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 n11 n12 Ry 3.29 x 1015 1/s
This suggests that the energy levels of the H atom are proportional to 1/n2
8 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 orbits.
Bohr postulates that there is Coulomb attraction between e- and nucleus. However classical physics is unable to explain why an H atom doesnt simply collapse.
9 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 (!) 10 The Bohr Model (cont.) Energy levels get closer together as n increases at n infinity E 0 11 The Bohr Model (cont.) We can use the Bohr model to predict what DE is for any two energy levels 12 The Bohr Model (cont.) Example At what wavelength will emission from n 4 to n 1 for the H atom be observed 1 4 13 The Bohr Model (cont.) Example What is the longest wavelength of light that will result in removal of the e- from H
1 14 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) Li2 (Z 3) etc. 15 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 16 Where does this go wrong
The Bohr models successes are limited
Doesnt 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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