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The Bohr Model of the Atom
The behavior of electrons in atoms is revealed by
the light given off when the electrons are “excited”
(made to absorb energy).
Johann Balmer showed that the visible series of lines from
the hydrogen spectrum obeyed the formula:
1 
 1
 (or )   2  2  for n  3, 4, 5....
2

n 
1
Niels Bohr explained all the various lines by
proposing that electrons in atoms could have only
certain energies, and that light was given off when
an electron underwent a transition from a higher
energy level to a lower one.
This leads to the following picture of what is
happening:
Bohr derived a more general formula to predict the
observed energies of light:
Each electron’s energy is determined by which level
it is in. The levels are designated by whole numbers, n.
 1
E  k  2 
n 
The energy cannot take any value, but has only
certain values depending on n.
Then for a change from one level to another,
the energy difference can be calculated:
What is frequency of light emitted from an electron undergoing a
transition from the n = 3 to the n = 2 level in the hydrogen atom?


1
1
E  2.18  10 18 J  2  2 
n

n
 f
i 
 2.18  10
18
1
 1
J 2  2 
2
3 
  3.03  10 19 J
Find the frequency of this light:
E

h

3.03  10 19 J
6.63  10  34 J  s
 4.57  1014 s 1
Find the wavelength of this light:

c


300
.  108 m / s
4.57  10 s
6.54  10 7
14
1
 6.54  10  7 m
 10 9 nm 
m
  654 nm
 1m 
Now, for what really happens. . .
For atoms with >1 electron, we must use a more complete
theory.
This theory, known as quantum mechanics, has more
quantum numbers than just n. Each electron is
characterized by n, and three other quantum numbers.
Here are the quantum numbers, and the values they can take:
n = 1, 2, 3 . . . (Principal quantum number)
l = 0, 1, 2 . . . (n – 1)
(Angular momentum quantum number)
(Determines shape of orbit)
ml = -l . . . . +l
(Magnetic quantum number)
(Determines orientation)
ms = +½ or -½
(Spin quantum number)
The energy and location of each electron in an atom is
determined by these numbers. Each electron has one
set: {n, l, ml, ms}.
Pauli exclusion principle:
Each electron in an atom must have a unique set of
the four quantum numbers.