If a bromine atom is available in the form of, say two isotopes, 79/35 Br (49.7%) and 81/35 Br (50.3%), calculate the average atomic mass of the bromine atom.
80.006 u
Explanation
The textbook explains that the accurate average atomic mass of an element must be calculated as a weighted average, which accounts for the natural abundances of its isotopes. A simple arithmetic mean would ignore the relative abundance of each isotope. By multiplying the mass of each isotope by its percent relative abundance and adding the results, we obtain the weighted average atomic mass of the element as it naturally occurs.
Solution Steps
Step 1: Identify the mass and percent relative abundance of the two isotopes. For ⁷⁹₃₅Br, Mass = 79 u, Abundance = 49.7%. For ⁸¹₃₅Br, Mass = 81 u, Abundance = 50.3%.
Step 2: Apply the weighted average atomic mass formula by multiplying the mass of each isotope by its percent relative abundance (divided by 100) and adding the values.
Step 3: Calculate the contribution of the first isotope: () / 100 = 39.263 u.
Step 4: Calculate the contribution of the second isotope: () / 100 = 40.743 u.
Step 5: Add the two values to find the average atomic mass: 39.263 u + 40.743 u = 80.006 u.