To calculate the average atomic mass of strontium using the given data, follow these steps:
1. List the given masses and their respective abundances:
- Isotope [tex]\( \text{Sr-84} \)[/tex]: Mass = 83.913428 amu, Abundance = 0.56%
- Isotope [tex]\( \text{Sr-86} \)[/tex]: Mass = 85.909273 amu, Abundance = 9.86%
- Isotope [tex]\( \text{Sr-87} \)[/tex]: Mass = 86.908902 amu, Abundance = 7.00%
- Isotope [tex]\( \text{Sr-88} \)[/tex]: Mass = 87.905625 amu, Abundance = 82.58%
2. Convert the percentage abundances into fractions:
- Abundance of [tex]\( \text{Sr-84} \)[/tex] = [tex]\( \frac{0.56}{100} = 0.0056 \)[/tex]
- Abundance of [tex]\( \text{Sr-86} \)[/tex] = [tex]\( \frac{9.86}{100} = 0.0986 \)[/tex]
- Abundance of [tex]\( \text{Sr-87} \)[/tex] = [tex]\( \frac{7.00}{100} = 0.0700 \)[/tex]
- Abundance of [tex]\( \text{Sr-88} \)[/tex] = [tex]\( \frac{82.58}{100} = 0.8258 \)[/tex]
3. Calculate the contribution of each isotope to the average atomic mass:
- Contribution of [tex]\( \text{Sr-84} \)[/tex] = [tex]\( 83.913428 \times 0.0056 = 0.470315 \)[/tex]
- Contribution of [tex]\( \text{Sr-86} \)[/tex] = [tex]\( 85.909273 \times 0.0986 = 8.467787 \)[/tex]
- Contribution of [tex]\( \text{Sr-87} \)[/tex] = [tex]\( 86.908902 \times 0.0700 = 6.083623 \)[/tex]
- Contribution of [tex]\( \text{Sr-88} \)[/tex] = [tex]\( 87.905625 \times 0.8258 = 72.598672 \)[/tex]
4. Sum up all these contributions to get the average atomic mass of strontium:
- Average atomic mass = [tex]\( 0.470315 + 8.467787 + 6.083623 + 72.598672 \)[/tex]
5. Calculate the final result:
- Average atomic mass = [tex]\( 87.620397 \)[/tex]
6. Round the result to two decimal places:
- Average atomic mass ≈ 87.62
Therefore, the average atomic mass of strontium is 87.62 amu.
