The Foundations of Chemistry

it emits exactly the same amount of energy it absorbed in moving from the lower to the
higher energy level. Figure 5-16 illustrates these transactions schematically. The values of
n 1 and n 2 in the Balmer-Rydberg equation identify the lower and higher levels, respec-
tively, of these electronic transitions.

The Danish physicist Niels Bohr was one of the most influential scientists of the twentieth
century. Like many other now-famous physicists of his time, he worked for a time in
England with J. J. Thomson and later with Ernest Rutherford. During this period, he began
to develop the ideas that led to the publication of his explanation of atomic spectra and his
theory of atomic structure, for which he received the Nobel Prize in 1922. After escaping
from German-occupied Denmark to Sweden in 1943, he helped to arrange the escape of
hundreds of Danish Jews from the Hitler regime. He later went to the United States, where,
until 1945, he worked with other scientists at Los Alamos, New Mexico, on the
development of the atomic bomb. From then until his death in 1962, he worked for the
development and use of atomic energy for peaceful purposes.

5-12 Atomic Spectra and the Bohr Atom 201

The Bohr Theory and the Balmer-Rydberg Equation

From mathematical equations describing the orbits for the hydrogen atom, together with
the assumption of quantization of energy, Bohr was able to determine two significant aspects
of each allowed orbit:

1.Wherethe electron can be with respect to the nucleus—that is, the radius, r, of the

circular orbit. This is given by

rn^2 a 0

where nis a positive integer (1, 2, 3,.. .) that tells which orbit is being described and

a 0 is the Bohr radius.Bohr was able to calculate the value of a 0 from a combination

of Planck’s constant, the charge of the electron, and the mass of the electron as

a 0 5.292 10 
^11 m0.5292 Å

2.How stablethe electron would be in that orbit—that is, its potential energy, E. This

is given by

E
 

82

h

m

2

a 02



where hPlanck’s constant, mthe mass of the electron, and the other symbols

have the same meaning as before. Eis always negative when the electron is in the

atom; E0 when the electron is completely removed from the atom (ninfinity).

Results of evaluating these equations for some of the possible values of n(1, 2, 3,.. .)
are shown in Figure 5-17. The larger the value of n, the farther from the nucleus is the
orbit being described, and the radius of this orbit increases as the square of nincreases. As
nincreases, n^2 increases, 1/n^2 decreases, and thus the electronic energy increases (becomes
less negative and smaller in magnitude). For orbits farther from the nucleus, the electronic
potential energy is higher (less negative—the electron is in a higherenergy level or in a less

2.180 10 
^18 J



n^2

1



n^2

E

nrichment

Note: ris proportional to n^2.

Note: Eis proportional to 


n

1

 2.

We define the potential energy of a set

of charged particles to be zero when

the particles are infinitely far apart.