Let's calculate the average atomic mass of strontium step-by-step. The average atomic mass is computed by multiplying the mass of each isotope by its natural abundance (in decimal form) and then summing these values.
Given data:
- Isotopes and their masses:
- [tex]\( \text{Sr-84}: 83.913428 \, \text{amu} \)[/tex]
- [tex]\( \text{Sr-86}: 85.909273 \, \text{amu} \)[/tex]
- [tex]\( \text{Sr-87}: 86.908902 \, \text{amu} \)[/tex]
- [tex]\( \text{Sr-88}: 87.905625 \, \text{amu} \)[/tex]
- Abundances (converted from percentage to decimal form):
- [tex]\( \text{Sr-84}: 0.0056 \)[/tex] (0.56% = 0.56 / 100 = 0.0056)
- [tex]\( \text{Sr-86}: 0.0986 \)[/tex] (9.86% = 9.86 / 100 = 0.0986)
- [tex]\( \text{Sr-87}: 0.0700 \)[/tex] (7.00% = 7.00 / 100 = 0.0700)
- [tex]\( \text{Sr-88}: 0.8258 \)[/tex] (82.58% = 82.58 / 100 = 0.8258)
Now, calculate the contribution of each isotope to the average atomic mass:
1. Contribution of [tex]\( \text{Sr-84} \)[/tex]:
[tex]\[
83.913428 \times 0.0056 = 0.46992 \, \text{amu}
\][/tex]
2. Contribution of [tex]\( \text{Sr-86} \)[/tex]:
[tex]\[
85.909273 \times 0.0986 = 8.47065 \, \text{amu}
\][/tex]
3. Contribution of [tex]\( \text{Sr-87} \)[/tex]:
[tex]\[
86.908902 \times 0.0700 = 6.08362 \, \text{amu}
\][/tex]
4. Contribution of [tex]\( \text{Sr-88} \)[/tex]:
[tex]\[
87.905625 \times 0.8258 = 72.59247 \, \text{amu}
\][/tex]
Finally, sum these contributions to get the average atomic mass:
[tex]\[
\text{Average atomic mass} = 0.46992 + 8.47065 + 6.08362 + 72.59247 = 87.62 \, \text{amu}
\][/tex]
The average atomic mass of strontium, rounded to two decimal places, is:
[tex]\[
\boxed{87.62} \, \text{amu}
\][/tex]
