To find a weighted average with isotopes and calculate the average atomic mass of an element, you need to consider the masses and relative abundances of each isotope. Here's a step-by-step procedure:
Identify the isotopes: Determine the isotopes of the element and their respective masses. Each isotope is identified by its mass number, which represents the total number of protons and neutrons in the nucleus.
Determine the relative abundances: Find the relative abundances of each isotope, which represent the percentage or fraction of that isotope in nature. This information is typically provided or can be obtained from reliable sources.
Calculate the weighted contribution: Multiply the mass of each isotope by its relative abundance to obtain the weighted contribution of each isotope to the average atomic mass. This step accounts for the fact that different isotopes occur in nature with different abundances.
Sum the weighted contributions: Add up the weighted contributions of all isotopes to find the total weighted average. This sum represents the average atomic mass of the element.
Here's an example using carbon isotopes:
Carbon has three naturally occurring isotopes: carbon-12, carbon-13, and carbon-14. Let's assume the relative abundances are approximately 98.9%, 1.1%, and a negligible amount (less than 0.01%) for each isotope, respectively.
Weighted contribution of carbon-12: 12.00 amu × 0.989 = 11.868 amu Weighted contribution of carbon-13: 13.00 amu × 0.011 = 0.143 amu Weighted contribution of carbon-14: 14.00 amu × 0.001 (negligible) = 0.000 amu
Summing the weighted contributions: 11.868 amu + 0.143 amu + 0.000 amu = 12.011 amu
Therefore, the average atomic mass of carbon is approximately 12.011 amu.
By following these steps, you can calculate the average atomic mass of an element by considering the masses and abundances of its isotopes.