Examine the table.

[tex]\[
\begin{tabular}{|c|c|c|}
\hline
Isotope & Atomic Mass & Abundance \\
\hline
${ }^{84}Sr$ & 83.913 & 0.56\% \\
\hline
${ }^{86}Sr$ & 85.909 & 9.86\% \\
\hline
${ }^{87}Sr$ & 86.909 & 7.00\% \\
\hline
${ }^{88}Sr$ & 87.906 & 82.58\% \\
\hline
\end{tabular}
\][/tex]

Based on the information provided for the isotopes of strontium (Sr), what is the average atomic mass of strontium?

A. 88.00 amu
B. 86.25 amu
C. 87.62 amu
D. [tex]$8.77 \times 10^3$[/tex] amu



Answer :

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.