Question

Strontium has four isotopes with the following masses: $$ 83.9134 \text { amu }(0.56 \%), 85.9094 \text { amu }(9.86 \%), 86.9089 \text { amu } $$ \((7.00 \%),\) and 87.9056 amu \((82.58 \%) .\) Calculate the average atomic mass of strontium.

Short answer

Answer: The average atomic mass of strontium is approximately 87.607 amu.

Step-by-step solution

Convert the percentages to decimals

To calculate the weighted average, we need to convert the abundance percentages to decimals. To do this, we will divide each percentage by 100: $$ 0.56\% = \frac{0.56}{100} = 0.0056\\ 9.86\% = \frac{9.86}{100} = 0.0986\\ 7.00\% = \frac{7.00}{100} = 0.07\\ 82.58\% = \frac{82.58}{100} = 0.8258 $$

Multiply each isotope's mass by its decimal abundance

Now that we have the decimal abundance of each isotope, we can multiply the mass of each isotope by its corresponding decimal abundance: $$ (83.9134\ \text{amu})(0.0056) = 0.470\\ (85.9094\ \text{amu})(0.0986) = 8.478\\ (86.9089\ \text{amu})(0.07) = 6.084\\ (87.9056\ \text{amu})(0.8258) = 72.575 $$

Add the products to find the average atomic mass

The last step is to add up the products we calculated in the previous step to find the average atomic mass of strontium: $$ 0.470 + 8.478 + 6.084 + 72.575 = \boxed{87.607\ \text{amu}} $$ The average atomic mass of strontium is approximately 87.607 amu.