Atomic Weight Example

Naturally occuring rubidium is 72.15% rubidium-85, with an atomic mass of 84.91 amu, and 27.85% rubidium-87, with an atomic mass of 86.79 amu.

What is the approximate atomic weight of rubidium?

Solution:

Wanted: The approximate atomic weight, or the average mass of a naturally occuring atom of rubidium.

Given:Rubidium occurs as 72.15% rubidium-85 and 27.85% rubidium-87. Suppose you have a sample of naturaly occuring rubidium that contains 10,000 atoms. (By using 10,000 atoms, our calculations will deal only in whole numbers of atoms.) You can calculate how many of the atoms are rubidium-85.

(72.15/100) x 10,000 atoms = 7,215 atoms of rubidium-85

The total mass of these atoms is:

7,215 atoms x (84.91 amu / 1 atom) = 6.126 x 10⁵ amu

You can also calculate the number f atoms of rubidium-87 and the total mass of these atoms.

(27.85/100) x 10,000 = 2,785 atoms of rubidium-87

2,785 atoms x (86.79 amu / 1 atom) = 2,417 x 10⁵ amu

The total mass of the sample is:

6.126 x 10⁵ amu + 2.417 x 10⁵ amu = 8.543 x 10⁵ amu

The average mass of a rubidium atom in the sample is:

(8.543 x 10⁵ amu / 10,000 atoms) = 85.43 amu (per atom)