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Chapter 3: Problem 39

An element consists of 1.40\(\%\) of an isotope with mass 203.973 u, 24.10\(\%\) of an isotope with mass 205.9745 u, 22.10\(\%\) of an isotope with mass 206.9759 u, and 52.40\(\%\) of an isotope with mass 207.9766 u. Calculate the average atomic mass, and identify the element.

Short Answer

Expert verified
The average atomic mass of the element is approximately 207.1673 u, and by comparing this value to known elements' atomic masses, we can identify the element as Lead (Pb).

Step by step solution

01

Convert percentages to decimals

To calculate the weighted average, we need to convert the given percentages of each isotope to decimals. To do this, we simply divide the percentage by 100. 1. 1.40% = 0.0140 2. 24.10% = 0.2410 3. 22.10% = 0.2210 4. 52.40% = 0.5240
02

Find the weighted average atomic mass

Now that we have the decimal values for each isotope's percentage, we can calculate the weighted average atomic mass by multiplying the mass of each isotope by its corresponding decimal value (percentage) and summing up the results: Weighted Average Atomic Mass = (0.0140 * 203.973 u) + (0.2410 * 205.9745 u) + (0.2210 * 206.9759 u) + (0.5240 * 207.9766 u) Weighted Average Atomic Mass = 2.855622 u + 49.6390945 u + 45.741979 u + 108.9806144 u Weighted Average Atomic Mass ≈ 207.1673 u
03

Identify the element

The calculated average atomic mass is approximately 207.1673 u. By comparing this value to the atomic mass of known elements, we can identify which element it is. In this case, the closest atomic mass is that of Lead (Pb) whose average atomic mass is approximately 207.2 u. Therefore, the element in question is Lead (Pb).

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