Isotope % Abundance Mass (amu)24
12 Mg 78.99 23.98504(^2512) Mg 10.00 24.98584
26
12 Mg 11.01 25.98259
Plan
We multiply the fraction of each isotope by its mass and add these numbers to obtain the
atomic weight of magnesium.
Solution
Atomic weight0.7899(23.98504 amu)0.1000(24.98584 amu)0.1101(25.98259 amu)
18.946 amu 2.4986 amu 2.8607 amu
24.30 amu (to four significant figures)
The two heavier isotopes make small contributions to the atomic weight of magnesium because
most magnesium atoms are the lightest isotope.
You should now work Exercises 26 and 28.
192 CHAPTER 5: The Structure of Atoms
Problem-Solving Tip:“Weighted” Averages
Consider the following analogy to the calculation of atomic weights. Suppose you want
to calculate the average weight of your classmates. Imagine that one half of them weigh
100 pounds each, and the other half weigh 200 pounds each. The average weight would
be
Average weight
1
2
(100 lb)
1
2
(200 lb)150 lb
Imagine, however, that three quarters of the class members weigh 100 pounds each, and
the other quarter weigh 200 pounds each. Now, the average weight would be
Average weight
3
4
(100 lb)
1
4
(200 lb)125 lb
We can express the fractions in this calculation in decimal form:
Average weight0.750(100 lb)0.250(200 lb)125 lb
In such a calculation, the value (in this case, the weight) of each thing (people, atoms)
is multiplied by the fraction of things that have that value. In Example 5-2 we expressed
each percentage as a decimal fraction, such as
78.99%
10
7
0
8.
p
9
a
9
rt
p
s
a
t
r
o
ts
tal
0.7899
Example 5-3 shows how the process can be reversed. Isotopic abundances can be calcu-
lated from isotopic masses and from the atomic weight of an element that occurs in nature
as a mixture of only two isotopes.