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:

( ) , , . . . .orn

for n1 1

2

13 4 5

2 2

Niels Bohr explained all the various lines by proposing that electrons in atoms could have onlycertain 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.

E kn

12

Then for a change from one level to another,the energy difference can be calculated:

The energy cannot take any value, but has onlycertain values depending on n.

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?

E Jn nf i

2 18 101 1182 2

.

2 18 101

2

1

33 03 1018

2 219. .J J

Find the frequency of this light:

E

h

J

J ss

3 03 10

6 63 104 57 10

19

3414 1.

..

Find the wavelength of this light:

c m s

sm

3 00 10

4 57 106 54 10

8

14 17. /

..

6 54 1010

16547

9

.

m

nm

mnm

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.