Answer :
To calculate the average atomic mass of strontium using the given isotopic masses and their abundances, follow these steps:
1. Convert the Abundance Percentages to Fractions:
We begin by converting the percentage abundances into decimal form (which allows us to work with them as fractions of the whole).
[tex]\[ \begin{aligned} \text{Abundance of } \ce{Sr-84} & = \frac{0.56}{100} = 0.0056, \\ \text{Abundance of } \ce{Sr-86} & = \frac{9.86}{100} = 0.0986, \\ \text{Abundance of } \ce{Sr-87} & = \frac{7.00}{100} = 0.07, \\ \text{Abundance of } \ce{Sr-88} & = \frac{82.58}{100} = 0.8258. \end{aligned} \][/tex]
2. Multiply Each Isotope's Mass by its Fractional Abundance:
Compute the product of each isotope's mass and its corresponding fractional abundance.
[tex]\[ \begin{aligned} \text{Contribution of } \ce{Sr-84} & = 83.913428 \times 0.0056 = 0.4703155968, \\ \text{Contribution of } \ce{Sr-86} & = 85.909273 \times 0.0986 = 8.4715725998, \\ \text{Contribution of } \ce{Sr-87} & = 86.908902 \times 0.07 = 6.08362314, \\ \text{Contribution of } \ce{Sr-88} & = 87.905625 \times 0.8258 = 72.590849442. \end{aligned} \][/tex]
3. Sum All Contributions to Get the Average Atomic Mass:
Add together all these contributions to find the overall average atomic mass of strontium.
[tex]\[ \begin{aligned} \text{Average Atomic Mass} & = 0.4703155968 + 8.4715725998 + 6.08362314 + 72.590849442 = 87.6166577796. \end{aligned} \][/tex]
4. Round the Result:
Finally, round the calculated average atomic mass to two decimal places.
[tex]\[ \text{Average Atomic Mass} \approx 87.62. \][/tex]
Thus, the average atomic mass of strontium, reported to two decimal places, is 87.62 amu.
1. Convert the Abundance Percentages to Fractions:
We begin by converting the percentage abundances into decimal form (which allows us to work with them as fractions of the whole).
[tex]\[ \begin{aligned} \text{Abundance of } \ce{Sr-84} & = \frac{0.56}{100} = 0.0056, \\ \text{Abundance of } \ce{Sr-86} & = \frac{9.86}{100} = 0.0986, \\ \text{Abundance of } \ce{Sr-87} & = \frac{7.00}{100} = 0.07, \\ \text{Abundance of } \ce{Sr-88} & = \frac{82.58}{100} = 0.8258. \end{aligned} \][/tex]
2. Multiply Each Isotope's Mass by its Fractional Abundance:
Compute the product of each isotope's mass and its corresponding fractional abundance.
[tex]\[ \begin{aligned} \text{Contribution of } \ce{Sr-84} & = 83.913428 \times 0.0056 = 0.4703155968, \\ \text{Contribution of } \ce{Sr-86} & = 85.909273 \times 0.0986 = 8.4715725998, \\ \text{Contribution of } \ce{Sr-87} & = 86.908902 \times 0.07 = 6.08362314, \\ \text{Contribution of } \ce{Sr-88} & = 87.905625 \times 0.8258 = 72.590849442. \end{aligned} \][/tex]
3. Sum All Contributions to Get the Average Atomic Mass:
Add together all these contributions to find the overall average atomic mass of strontium.
[tex]\[ \begin{aligned} \text{Average Atomic Mass} & = 0.4703155968 + 8.4715725998 + 6.08362314 + 72.590849442 = 87.6166577796. \end{aligned} \][/tex]
4. Round the Result:
Finally, round the calculated average atomic mass to two decimal places.
[tex]\[ \text{Average Atomic Mass} \approx 87.62. \][/tex]
Thus, the average atomic mass of strontium, reported to two decimal places, is 87.62 amu.
