To calculate the atomic mass of an element with two isotopes, you need to use a weighted average based on the mass and relative abundance of each isotope.
Here's a step-by-step breakdown:
1. Understand the Terms:
- Isotopes: Atoms of the same element that have different numbers of neutrons, and therefore different mass numbers.
- Mass Number: The total number of protons and neutrons in an atom's nucleus.
- Atomic Mass: The weighted average mass of all isotopes of an element, expressed in atomic mass units (amu).
- Relative Abundance: The percentage or proportion of each isotope that exists naturally. This is often given as a percentage but needs to be converted to a decimal for calculation.
2. Gather the Required Information:
You need the following for each isotope:
- Mass of Isotope: The actual mass of each isotope (usually given in amu).
- Relative Abundance of Isotope: The percentage of each isotope found in nature.
3. Convert Percentages to Decimals:
If the relative abundances are given as percentages, divide each percentage by 100 to convert it to a decimal. For example, 75% becomes 0.75.
4. Calculation:
The formula to calculate the atomic mass is:
Atomic Mass = (Mass of Isotope 1 × Relative Abundance of Isotope 1) + (Mass of Isotope 2 × Relative Abundance of Isotope 2)
5. Example:
Let's say we have an element, X, with two isotopes:
- Isotope X-20 has a mass of 19.992 amu and a relative abundance of 75%.
- Isotope X-22 has a mass of 21.990 amu and a relative abundance of 25%.
Here's how to calculate the atomic mass of element X:
- Convert percentages to decimals: 75% = 0.75 and 25% = 0.25.
- Apply the formula:
Atomic Mass = (19.992 amu × 0.75) + (21.990 amu × 0.25)
Atomic Mass = 14.994 amu + 5.4975 amu
Atomic Mass = 20.4915 amu
Therefore, the atomic mass of element X is approximately 20.4915 amu.
In summary, to find the atomic mass of an element with two isotopes, multiply the mass of each isotope by its relative abundance (expressed as a decimal), and then add the results together. This weighted average reflects the proportion of each isotope found in nature.
