Isotopes are used to determine the average atomic mass by considering both their individual masses and their relative abundances in nature.
Here's a breakdown of the process:
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Isotopes and Atomic Mass: Isotopes are variants of a chemical element which share the same number of protons and electrons, but have different numbers of neutrons. Because of the difference in neutron number, isotopes have differing atomic masses. The atomic mass of an individual isotope is usually close to its mass number (the total number of protons and neutrons in the nucleus).
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Relative Abundance: The relative abundance of an isotope is the percentage of atoms of an element that exist as a particular isotope. These abundances are experimentally determined and reflect how common each isotope is in a naturally occurring sample of the element.
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Calculation: The average atomic mass is calculated as a weighted average of the masses of each isotope, where the weight is the relative abundance. The formula is as follows:
Average Atomic Mass = (Mass of Isotope 1 × Relative Abundance of Isotope 1) + (Mass of Isotope 2 × Relative Abundance of Isotope 2) + ... + (Mass of Isotope N × Relative Abundance of Isotope N)
Where:
- "Mass of Isotope" is the atomic mass of each specific isotope.
- "Relative Abundance" is the decimal form of the percentage abundance (e.g., 75% becomes 0.75).
Example:
Let's say we have an element with two isotopes:
- Isotope 1: Mass = 20 amu, Abundance = 90%
- Isotope 2: Mass = 22 amu, Abundance = 10%
The average atomic mass would be:
(20 amu × 0.90) + (22 amu × 0.10) = 18 amu + 2.2 amu = 20.2 amu
Therefore, the average atomic mass of this element is 20.2 amu. This value is what you would typically find on the periodic table.
In essence, isotopes' individual masses and abundances are critical data points that, when combined through a weighted average calculation, accurately reflect the element's average atomic mass, accounting for the existence of multiple isotopes in a naturally occurring sample.
