Bohr Model of the Atom

1
Bohr Model of the Atom

• Outline
• Emission spectrum of atomic hydrogen.
• The Bohr model.
• Extension to higher atomic number.

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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
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Emission spectrum of H

• Continuous spectrum

• Quantized spectrum

DE
DE
Any DE is possible
Only certain DE are allowed
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Emission spectrum of H (cont.)
Light Bulb
Hydrogen Lamp
Quantized not continuous
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Emission spectrum of H (cont.)
We can use the emission spectrum to determine the
energy levels for the hydrogen atom.
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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.

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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

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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.

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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 (!)
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The Bohr Model (cont.)
Energy levels get closer together as n
increases
at n infinity E 0
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The Bohr Model (cont.)
We can use the Bohr model to predict what DE
is for any two energy levels
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The Bohr Model (cont.)
Example At what wavelength will emission
from n 4 to n 1 for the H atom be
observed
1
4
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The Bohr Model (cont.)
Example What is the longest wavelength of
light that will result in removal of the e- from
H

1
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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.
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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
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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.