Using the information in the table, calculate the average atomic mass of strontium. Report to two decimal places.
[tex] \square [/tex] amu
| Strontium |
|---|---|---|
| Isotope | Mass (amu) | Abundance |
| Sr-84 | 83.913428 | 0.56% |
| Sr-86 | 85.909273 | 9.86% |
| Sr-87 | 86.908902 | 7.00% |
| Sr-88 | 87.905625 | 82.58%
Answer (2)
Multiply the mass of each isotope by its abundance (as a decimal).
Sum the results from the previous step: ( 83.913428 amu × 0.0056 ) + ( 85.909273 amu × 0.0986 ) + ( 86.908902 amu × 0.0700 ) + ( 87.905625 amu × 0.8258 ) = 87.6266582 amu .
Round the result to two decimal places.
The average atomic mass of strontium is 87.63 amu .
Explanation
Problem Analysis We are given the mass and abundance of four isotopes of strontium and asked to calculate the average atomic mass of strontium. The average atomic mass is the weighted average of the masses of the isotopes, where the weights are the abundances of the isotopes.
Calculation Method To calculate the average atomic mass, we multiply the mass of each isotope by its abundance (expressed as a decimal) and then sum the results.
Isotope Data The masses and abundances are: Sr-84: 83.913428 amu, 0.56% (0.0056) Sr-86: 85.909273 amu, 9.86% (0.0986) Sr-87: 86.908902 amu, 7.00% (0.0700) Sr-88: 87.905625 amu, 82.58% (0.8258)
Weighted Average Calculation Now, we calculate the weighted average: ( 83.913428 amu × 0.0056 ) + ( 85.909273 amu × 0.0986 ) + ( 86.908902 amu × 0.0700 ) + ( 87.905625 amu × 0.8258 ) = 0.4699152 + 8.4716693 + 6.0836231 + 72.6014506
Summing and Rounding Adding these values together, we get: 0.4699152 + 8.4716693 + 6.0836231 + 72.6014506 = 87.6266582 amu Rounding to two decimal places, we get 87.63 amu.
Final Answer Therefore, the average atomic mass of strontium is approximately 87.63 amu.
Examples
Understanding average atomic mass is crucial in various fields. For instance, in environmental science, it helps in tracing the origin and movement of pollutants. If strontium isotopes are found in soil samples, knowing their average atomic mass can help scientists determine the source of the contamination, whether it's from industrial waste or natural deposits. This knowledge aids in implementing effective remediation strategies and protecting ecosystems.
The average atomic mass of strontium is calculated by multiplying the mass of each isotope by its relative abundance (as a decimal), summing these products, and rounding to two decimal places. The final result is approximately 87.63 amu. This value reflects the weighted contributions of all isotopes of strontium.
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