Final answer:
Calculating the average atomic mass of an element involves using the weighted average formula, where each isotope's mass is multiplied by its fractional natural abundance and then summed together. This reflects the natural variation of isotopes in a sample of the element.
Step-by-step explanation:
To calculate the average atomic mass of an element, you need the relative abundances of the element's naturally occurring isotopes and the masses of those isotopes. The formula to find the average atomic mass is the sum of the products of each isotope's mass (Mi) and its fractional abundance (fi). This calculation gives a weighted average because it takes into account the different proportions in which each isotope occurs naturally.
The periodic table provides the atomic mass as the weighted average of the isotopic masses, which approximates the value derived from the summation of each isotope's mass multiplied by its fractional abundance. In many cases, the atomic mass you will find on the periodic table will be closer to the mass of the most abundant isotope due to its significant influence on the overall weight.
A practical example would be an element with two isotopes A and B with masses of 10 u and 11 u, and relative abundances of 50% each. The calculation would be (0.50 x 10 u) + (0.50 x 11 u), which equals a weighted average atomic mass of 10.5 u for that element.