Abundance of isotopes
The atomic mass for each element is reported on the periodic table. This number is a weighted
average of the masses of each of the isotopes of an element. For example, the atomic mass of carbon is
reported as 12.011 amu. Carbon is composed primarily of two isotopes: carbon-12 and carbon-13. The
atomic mass is calculated from the relative abundance and the masses for these two isotopes. Using the
equation below we can calculate the atomic mass for carbon.
Atomic Mass = % isotope 1 × mass isotope 1 + % isotope 2 × mass isotope 2 +……..
Sample problem:
Carbon-12 makes up 98.93% of all of the carbon atoms, while carbon-13 is about 1.07% abundant.
Since the carbon-12 isotope is more abundant, its mass is weighted more in the calculation of
carbon’s atomic mass. An example calculation is done below.
Isotope
Carbon-12
Carbon-13
%
98.93%
1.07%
Abundance Mass
12.000 amu
13.003 amu
85
87
1. Rubidium is a soft, silvery-white metal that has two common isotopes, Rb and Rb. If the abundance of
85
87
Rb is 72.2% and the abundance of Rb is 27.8%, what is the average atomic mass of rubidium? ( Ans:
85.56 amu)
2. Uranium is used in nuclear reactors and is a rare element on earth. Uranium has three common isotopes. If
234
235
238
the abundance of U is 0.01%, the abundance of U is 0.71%, and the abundance of U is 99.28%,
what is the average atomic mass of uranium? (Ans: 237.98 amu)
63
65
63
3. Copper used in electric wires comes in two flavors (isotopes): Cu and Cu. Cu has an atomic mass
65
of 62.9298 amu and an abundance of 69.09%. The other isotope, Cu, has an abundance of 30.91%.
The average atomic mass between these two isotopes is 63.546 amu. Calculate the actual atomic
65
mass of Cu. ( Ans: 64.9278 amu)
4.
Complete the table Isotope
Neon-20
Neon-21
Neon-22
Mass (amu)
19.992
20.994
Avg. Atomic Mass =
Relative Abundance (%)
90.51
9.22
Total %:
5. Silver (Atomic weight 107.868) has two naturally-occurring isotopes with isotopic weights of
106.90509 and 108.90470. What is the percentage abundance of the lighter isotope?
6.
An imaginary element (Atomic weight 93.7140) has three naturally-occurring isotopes with
isotopic weights of 92.9469, 93.2923 and 94.9030. The abundance of the lightest isotope is 42.38
%. What is the percentage abundance of the heaviest isotope?
In this case, we know the abundance of one of the isotopes. We know the percentages of the lighter
isotope (42.38 %) and the percentage of the heavier isotope (x), so the percentage of the middle
isotope is equal to 1 (100%) minus the other two percentages (1 - 0.4238 - x).
92.9469 (0.4238) + 93.2923 [(1-0.4238)-x] + 94.9030x = 93.7140
39.3909 + 53.7550 - 93.2923x + 94.9030x = 93.7140
93.14 + 1.6107x = 93.7140
1.6107x = 0.4217
x = 26.18