1. Lecture 17: 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. 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 J
Emission

3. Emission spectrum of H “Continuous” spectrum “Quantized” spectrum 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 = n1+1, n1+2, …
Ry = 3.29 x /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 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.

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 = x 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), Li+2 (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 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.