To calculate the average atomic mass of strontium using the given data, we can follow these steps:
1. List the masses and abundances of the isotopes:
- [tex]\( Sr-84 \)[/tex]: Mass = 83.913428 amu, Abundance = 0.56%
- [tex]\( Sr-86 \)[/tex]: Mass = 85.909273 amu, Abundance = 9.86%
- [tex]\( Sr-87 \)[/tex]: Mass = 86.908902 amu, Abundance = 7.00%
- [tex]\( Sr-88 \)[/tex]: Mass = 87.905625 amu, Abundance = 82.58%
2. Convert the percentage abundances to fractions:
- [tex]\( Sr-84 \)[/tex]: [tex]\( 0.56\% = \frac{0.56}{100} = 0.0056 \)[/tex]
- [tex]\( Sr-86 \)[/tex]: [tex]\( 9.86\% = \frac{9.86}{100} = 0.0986 \)[/tex]
- [tex]\( Sr-87 \)[/tex]: [tex]\( 7.00\% = \frac{7.00}{100} = 0.0700 \)[/tex]
- [tex]\( Sr-88 \)[/tex]: [tex]\( 82.58\% = \frac{82.58}{100} = 0.8258 \)[/tex]
3. Multiply each isotope's mass by its fractional abundance:
- [tex]\( Sr-84 \)[/tex]: [tex]\( 83.913428 \times 0.0056 \)[/tex]
- [tex]\( Sr-86 \)[/tex]: [tex]\( 85.909273 \times 0.0986 \)[/tex]
- [tex]\( Sr-87 \)[/tex]: [tex]\( 86.908902 \times 0.0700 \)[/tex]
- [tex]\( Sr-88 \)[/tex]: [tex]\( 87.905625 \times 0.8258 \)[/tex]
4. Sum these products to find the average atomic mass:
[tex]\[
\text{Average atomic mass} = (83.913428 \times 0.0056) + (85.909273 \times 0.0986) + (86.908902 \times 0.0700) + (87.905625 \times 0.8258)
\][/tex]
5. Calculate each term separately:
- [tex]\( 83.913428 \times 0.0056 = 0.4703155968 \)[/tex]
- [tex]\( 85.909273 \times 0.0986 = 8.4707100878 \)[/tex]
- [tex]\( 86.908902 \times 0.0700 = 6.08362314 \)[/tex]
- [tex]\( 87.905625 \times 0.8258 = 72.592008955 \)[/tex]
6. Sum the calculated products:
[tex]\[
0.4703155968 + 8.4707100878 + 6.08362314 + 72.592008955 = 87.6166577796
\][/tex]
7. Round the result to two decimal places:
[tex]\[
87.6166577796 \approx 87.62
\][/tex]
Therefore, the average atomic mass of strontium is [tex]\( 87.62 \)[/tex] amu.
