To calculate the average atomic mass of strontium, follow these steps:
1. Convert the percentage abundances to decimal form:
- For [tex]\( Sr-84 \)[/tex]: [tex]\( 0.56\% \)[/tex] becomes [tex]\( 0.56 \div 100 = 0.0056 \)[/tex].
- For [tex]\( Sr-86 \)[/tex]: [tex]\( 9.86\% \)[/tex] becomes [tex]\( 9.86 \div 100 = 0.0986 \)[/tex].
- For [tex]\( Sr-87 \)[/tex]: [tex]\( 7.00\% \)[/tex] becomes [tex]\( 7.00 \div 100 = 0.07 \)[/tex].
- For [tex]\( Sr-88 \)[/tex]: [tex]\( 82.58\% \)[/tex] becomes [tex]\( 82.58 \div 100 = 0.8258 \)[/tex].
2. Multiply the mass of each isotope by its respective abundance:
- For [tex]\( Sr-84 \)[/tex]: [tex]\( 83.913428 \times 0.0056 = 0.4703155968 \)[/tex]
- For [tex]\( Sr-86 \)[/tex]: [tex]\( 85.909273 \times 0.0986 = 8.467713638 \)[/tex]
- For [tex]\( Sr-87 \)[/tex]: [tex]\( 86.908902 \times 0.07 = 6.08362314 \)[/tex]
- For [tex]\( Sr-88 \)[/tex]: [tex]\( 87.905625 \times 0.8258 = 72.594999404 \)[/tex]
3. Sum these values to get the total average atomic mass:
[tex]\[
0.4703155968 + 8.467713638 + 6.08362314 + 72.594999404 = 87.6166577796\: \text{amu}
\][/tex]
4. Round the average atomic mass to two decimal places:
[tex]\[
87.6166577796 \approx 87.62\: \text{amu}
\][/tex]
Therefore, the average atomic mass of strontium is [tex]\( 87.62 \)[/tex] amu when rounded to two decimal places.
