To calculate the atomic mass of strontium based on its isotopes and their respective abundances, we use the following formula:
\[ \text{Atomic Mass} = \sum (\text{mass of isotope} \times \text{fractional abundance}) \]
First, let's convert the percentages into fractions:
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For \(\text{Sr}^{84}\):
- Mass: 84
- Abundance: 0.50% = 0.0050
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For \(\text{Sr}^{86}\):
- Mass: 86
- Abundance: 9.9% = 0.099
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For \(\text{Sr}^{87}\):
- Mass: 87
- Abundance: 7.0% = 0.070
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For \(\text{Sr}^{88}\):
- Mass: 88
- Abundance: 82.6% = 0.826
Now we can calculate the contributions of each isotope to the atomic mass:
\[ \text{Contribution of } \text{Sr}^{84} = 84 \times 0.0050 = 0.42 \] \[ \text{Contribution of } \text{Sr}^{86} = 86 \times 0.099 = 8.514 \] \[ \text{Contribution of } \text{Sr}^{87} = 87 \times 0.070 = 6.09 \] \[ \text{Contribution of } \text{Sr}^{88} = 88 \times 0.826 = 72.728 \]
Now sum all the contributions together:
\[ \text{Total Atomic Mass} = 0.42 + 8.514 + 6.09 + 72.728 = 87.752 \]
Therefore, the atomic mass of strontium (Sr) is approximately 87.75 u (atomic mass units).
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