October 23, 2009
• T H E B O H R M O D E L O F T H E A T O M

The Bohr Model of Hydrogen Atom



Light absorbed or emitted is from electrons moving between energy levels
Only certain energies are observed
Therefore, only certain energy levels exist

Energy levels are Quantized

Absorption and Emission Spectra

Hydrogen Energy Levels

Constant
Constant = Rhc = 2.18 x 10 -18 J
R = Rydberg constant = 1.0974 x 10 7 m -1
 -34 Js c= velocity of light in vacuum = 3.0 x 10 8 m/s



Each line corresponds to a transition:
Example: n=3  n = 2
E
3
 
2.18 x 10
-18
J
3
2
 


19
J
 E
 hc

E
2
 
2.18 x 10
-18
J
 
5.45
x 10

19
J
E photon
 
E

E final
 
5.45
x 10

19

J
E
 initial
(


E
2.42
x
2

E

10

19
3
J )
 
3.03
x 10

19
J
  hc
E photon

(6.626
x 10

34
J
 s )(3.0
x 10
8 m / s )

3.03
x 10

19
J
 
6.56
x 10

7 m

656 nm


Explanation of line spectra
Balmer series

The emission line with the shortest wavelength is:
1.
4.
5.
2.
3.
1
2
3
4
5

The emission line with the longest wavelength is:
1.
4.
5.
2.
3.
1
2
3
4
5

The emission line with the highest energy is:
1.
4.
5.
2.
3.
1
2
3
4
5

The absorption line with the shortest wavelength is:
1.
4.
5.
2.
3.
1
2
3
4
5

The absorption line with the lowest energy is:
1.
4.
5.
2.
3.
1
2
3
4
5

A Revolutionary Idea: Matter Waves
 All matter acts as particles and as waves.
 Macroscopic objects have tiny waves- not observed.
 Wave nature only becomes apparent when object is VERY light
 For electrons in atoms, wave properties are important.
 deBroglie Equation:
  h m  v



Matter waves- Examples
Macroscopic object: 200 g rock travelling at 20 m/s has a wavelength:
  h m
 v

6.626
x 10

34
J
 s

1.66
x 10

34 m
(0.2
kg )(20 m / s )
Electron inside an atom, moving at 40% of the speed of light (0.4 x 3x10 8 m/s):

  h m
 v

6.626
x 10

34
J
 s
(9.11
x 10

31 kg )(0.4)(3.0
x 10
8 m / s )

6.06
x 10

12 m

0.006
nm

Can see matter waves in experiments