The Foundations of Chemistry

EXAMPLE 5-3 Calculation of Isotopic Abundance

The atomic weight of gallium is 69.72 amu. The masses of the naturally occurring isotopes
are 68.9257 amu for^6931 Ga and 70.9249 amu for^7131 Ga. Calculate the percent abundance of each
isotope.

Plan

We represent the fraction of each isotope algebraically. Atomic weight is the weighted average
of the masses of the constituent isotopes. So the fraction of each isotope is multiplied by its
mass, and the sum of the results is equal to the atomic weight.

Solution

Let xfraction of^6931 Ga. Then (1
x)fraction of^7131 Ga.

x(68.9257 amu)(1
x)(70.9249 amu)69.72 amu

68.9257x70.9249
70.9249x69.72


1.9992x
1.20

x0.600

x0.600fraction of^6931 Ga 
 60.0%^6931 Ga

(1
x)0.400fraction of^7131 Ga 
 40.0%^7131 Ga

You should now work Exercise 30.

THE ELECTRONIC STRUCTURES OF ATOMS

The Rutherford model of the atom is consistent with the evidence presented so far, but
it has some serious limitations. It does not answer such important questions as: Whydo
different elements have such different chemical and physical properties? Whydoes chem-
ical bonding occur at all? Whydoes each element form compounds with characteristic
formulas? Howcan atoms of different elements give off or absorb light only of charac-
teristic colors (as was known long before 1900)?
To improve our understanding, we must first learn more about the arrangements of
electrons in atoms. The theory of these arrangements is based largely on the study of the
light given off and absorbed by atoms. Then we will develop a detailed picture of the elec-
tron configurationsof different elements. A knowledge of these arrangements will help us
to understand the periodic table and chemical bonding.

ELECTROMAGNETIC RADIATION

Our ideas about the arrangements of electrons in atoms have evolved slowly. Much of the
information has been derived from atomic emission spectra.These are the lines, or
bands, produced on photographic film by radiation that has passed through a refracting
glass prism after being emitted from electrically or thermally excited atoms. To help us
understand the nature of atomic spectra, we first describe electromagnetic radiation.
All types of electromagnetic radiation, or radiant energy, can be described in the termi-
nology of waves. To help characterize any wave, we specify its wavelength(or its frequency).

5-10

When a quantity is represented by

fractions, the sum of the fractions

must always be unity. In this case,

x(1
x)1.

5-1 0Electromagnetic Radiation 193

White light is dispersed by a prism

into a continuousspectrum.

See the Saunders Interactive

General Chemistry CD-ROM,

Screen 7.3, Electromagnetic Radiation.