To determine the average atomic mass of the element given its isotopes and their respective abundances, we follow these steps:
1. List the mass and abundance of each isotope.
Here, we have:
- Isotope with mass 20.0 amu and abundance 90.480%
- Isotope with mass 21.0 amu and abundance 0.270%
- Isotope with mass 22.0 amu and abundance 9.250%
2. Convert the percentages into fractions (i.e., divide each percentage by 100).
- 90.480% becomes 0.90480
- 0.270% becomes 0.00270
- 9.250% becomes 0.09250
3. Multiply the mass of each isotope by its fractional abundance to find the weighted contribution of each isotope to the average atomic mass.
- For the isotope with mass 20.0 amu:
[tex]\[
20.0 \times 0.90480 = 18.096
\][/tex]
- For the isotope with mass 21.0 amu:
[tex]\[
21.0 \times 0.00270 = 0.0567
\][/tex]
- For the isotope with mass 22.0 amu:
[tex]\[
22.0 \times 0.09250 = 2.035
\][/tex]
4. Sum these contributions to get the average atomic mass.
[tex]\[
\text{Average atomic mass} = 18.096 + 0.0567 + 2.035 = 20.1877
\][/tex]
So, the average atomic mass of the element is [tex]\(20.1877 \text{ amu}\)[/tex].
