To find the average atomic mass of strontium based on the given isotopes and their abundances, we can use the concept of a weighted average. The average atomic mass is calculated by summing the products of the atomic masses of each isotope and their respective abundances. Here's the step-by-step solution:
1. List the provided data:
- For [tex]\( ^{84}Sr \)[/tex]:
- Atomic Mass = 83.913
- Abundance = 0.56%
- For [tex]\( ^{86}Sr \)[/tex]:
- Atomic Mass = 85.909
- Abundance = 9.86%
- For [tex]\( ^{87}Sr \)[/tex]:
- Atomic Mass = 86.909
- Abundance = 7.00%
- For [tex]\( ^{88}Sr \)[/tex]:
- Atomic Mass = 87.906
- Abundance = 82.58%
2. Convert the abundances from percentages to decimals:
- 0.56% = 0.0056
- 9.86% = 0.0986
- 7.00% = 0.0700
- 82.58% = 0.8258
3. Multiply the atomic mass of each isotope by its decimal abundance:
- [tex]\( ^{84}Sr \)[/tex]: [tex]\( 83.913 \times 0.0056 \)[/tex]
- [tex]\( ^{86}Sr \)[/tex]: [tex]\( 85.909 \times 0.0986 \)[/tex]
- [tex]\( ^{87}Sr \)[/tex]: [tex]\( 86.909 \times 0.0700 \)[/tex]
- [tex]\( ^{88}Sr \)[/tex]: [tex]\( 87.906 \times 0.8258 \)[/tex]
4. Calculate those products:
- [tex]\( 83.913 \times 0.0056 = 0.470312 \)[/tex]
- [tex]\( 85.909 \times 0.0986 = 8.4666914 \)[/tex]
- [tex]\( 86.909 \times 0.0700 = 6.08363 \)[/tex]
- [tex]\( 87.906 \times 0.8258 = 72.596311 \)[/tex]
5. Sum the results of these products to find the average atomic mass:
- [tex]\( 0.470312 + 8.4666914 + 6.08363 + 72.596311 = 87.6169454 \)[/tex]
6. Round, if necessary, to match provided choices:
- [tex]\( 87.616945 \approx 87.62 \)[/tex]
Thus, the average atomic mass of strontium based on the provided isotopes and their abundances is 87.62 amu.
