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Chapter 2: Problem 110

The four naturally occurring isotopes of strontium have the atomic masses 83.9134 u; 85.9093 u; 86.9089 u; and 87.9056 u. The percent natural abundance of the lightest isotope is \(0.56 \%\) and of the heaviest, \(82.58 \%\) Estimate the percent natural abundances of the other two. Why is this result only a rough approximation?

Short Answer

Expert verified
The estimated percent natural abundances for these two isotopes of strontium are approximately 4.20% for the 85.9093 u isotope and 4.25% for the 86.9089 u isotope. The result is a rough approximation because the exact percent abundances depend on various factors, including the location where the strontium is found, and not merely on the atomic masses of the isotopes.

Step by step solution

01

Identify Given Values

The atomic masses for the isotopes are given as 83.9134 u, 85.9093 u, 86.9089 u, and 87.9056 u. The percent natural abundance of the lightest isotope (83.9134 u) is 0.56%, and of the heaviest (87.9056 u) is 82.58%.
02

Calculate the Remaining Abundance

Knowing that the total natural abundances of all isotopes add up to 100%, you can calculate the remaining abundance to be distributed among the other two isotopes. That is \(100\% - 0.56\% - 82.58\% = 16.86\%\).
03

Calculate the Proportions Compared to the Total Mass

Now, calculate the total atomic mass: \(83.9134 u + 85.9093 u + 86.9089 u + 87.9056 u = 344.6372 u\). Determine the proportion of the atomic mass for each of the two isotopes in question to the total mass. For the 85.9093 u isotope, the proportion is \(85.9093 u / 344.6372 u = 0.2491\). For the 86.9089 u isotope, the proportion is \(86.9089 u / 344.6372 u = 0.2522\).
04

Calculate the Estimated Percent Natural Abundances

Multiply the proportions calculated in the previous step by the remaining percent abundance to estimate the percent natural abundances of the other two isotopes. For the 85.9093 u isotope, the estimate is \(0.2491 * 16.86 \% = 4.20 \%\). For the 86.9089 u isotope, the estimate is \(0.2522 * 16.86 \% = 4.25 \%\).

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