- Convert all percentage abundances to decimal form by dividing by 100.
- Multiply each isotope's mass by its decimal abundance to find its contribution.
- Sum the individual contributions to get the total average atomic mass.
- Round the result to two decimal places to get \(\boxed{87.62 \text{ amu}}\).
Explanation
- Analysis of Isotope Data
To find the average atomic mass of strontium, we consider the contribution of each isotope to the total mass based on its relative abundance. We are given the masses and percentage abundances for four isotopes:
- Sr-84: mass \(= 83.913428\) amu, abundance \(= 0.56\%\)
- Sr-86: mass \(= 85.909273\) amu, abundance \(= 9.86\%\)
- Sr-87: mass \(= 86.908902\) amu, abundance \(= 7.00\%\)
- Sr-88: mass \(= 87.905625\) amu, abundance \(= 82.58\%\)
First, we verify that the sum of the abundances is \(0.56\% + 9.86\% + 7.00\% + 82.58\% = 100.00\%\), which confirms the data is complete.
- Weighted Average Calculation
To calculate the average atomic mass, we convert the percentage abundances into decimal form by dividing each percentage by 100:
- Abundance of Sr-84 \(= 0.0056\)
- Abundance of Sr-86 \(= 0.0986\)
- Abundance of Sr-87 \(= 0.0700\)
- Abundance of Sr-88 \(= 0.8258\)
The weighted average atomic mass is calculated using the formula:
\[\text{Average Atomic Mass} = \sum (\text{Mass}_i \times \text{Abundance}_i)\]
Calculating each contribution:
- Sr-84: \(83.913428 \times 0.0056 \approx 0.469915\)
- Sr-86: \(85.909273 \times 0.0986 \approx 8.470654\)
- Sr-87: \(86.908902 \times 0.0700 \approx 6.083623\)
- Sr-88: \(87.905625 \times 0.8258 \approx 72.592465\)
- Final Summation and Rounding
Summing these contributions gives the weighted average atomic mass:
\[0.469915 + 8.470654 + 6.083623 + 72.592465 = 87.616657\]
Rounding this value to two decimal places, we obtain:
\[87.616657 \approx 87.62\]
Thus, the average atomic mass of strontium is \(\boxed{87.62 \text{ amu}}\).
Examples
The concept of weighted average atomic mass is essential in chemistry for understanding the properties of elements. In real life, it is used by pharmaceutical researchers when calculating dosages based on the naturally occurring isotopes of elements present in medications, ensuring precise and safe treatments. It also helps in geological dating, where scientists analyze strontium isotope ratios to determine the age of rocks and minerals in the Earth's crust.