The Foundations of Chemistry

When an electric current is passed through hydrogen gas at very low pressures, several

series of lines in the spectrum of hydrogen are produced. These lines were studied intensely

by many scientists. In the late nineteenth century, Johann Balmer (1825–1898) and

Johannes Rydberg (1854–1919) showed that the wavelengths of the various lines in the

hydrogen spectrum can be related by a mathematical equation:

R


Here Ris 1.097 107 m
^1 and is known as the Rydberg constant. The n’s are positive

integers, and n 1 is smaller than n 2. The Balmer-Rydberg equation was derived from

numerous observations, not theory. It is thus an empirical equation.

In 1913, Niels Bohr (1885–1962), a Danish physicist, provided an explanation for

Balmer and Rydberg’s observations. He wrote equations that described the electron of a

hydrogen atom as revolving around its nucleus in circular orbits. He included the assump-

tion that the electronic energy is quantized;that is, only certain values of electronic energy

are possible. This led him to suggest that electrons can only be in certain discrete orbits,

and that they absorb or emit energy in discrete amounts as they move from one orbit to

another. Each orbit thus corresponds to a definite energy levelfor the electron. When an

electron is promoted from a lower energy level to a higher one, it absorbs a definite (or

quantized) amount of energy. When the electron falls back to the original energy level,

1



n 22

1



n 12

1





The lightning flashes produced in
electrical storms and the light
produced by neon gas in neon signs
are two familiar examples of visible
light produced by electronic
transitions.

200 CHAPTER 5: The Structure of Atoms

Figure 5-16 (a) The radii of the first four Bohr orbits for a hydrogen atom. The dot at

the center represents the nuclear position. The radius of each orbit is proportional to n^2 ,

so these four are in the ratio 1 4  9 16. (b) Relative values for the energies associated with

the various energy levels in a hydrogen atom. The energies become closer together as n

increases. They are so close together for large values of nthat they form a continuum. By

convention, potential energy is defined as zero when the electron is at an infinite distance

from the atom. Any more stable arrangement would have a lower energy. Potential energies

of electrons in atoms are therefore always negative. Some possible electronic transitions

corresponding to lines in the hydrogen emission spectrum are indicated by arrows.

Transitions in the opposite directions account for lines in the absorption spectrum.

n = 1 n = 2

n = 3

n = 4

n = 3

n = 2

n = 1

n = 4

n = 5

(^0) n = ∞
Potential energy
(b)
(a)
(b)
(a)
See the Saunders Interactive
General Chemistry CD-ROM,
Screen 7.7, Bohr’s Model of the
Hydrogen Atom.