17. Identify the element based on the following values for its three isotopes: 179.947 amu (0.12% ) 181.948 amu (26.50% ) , 182.950 amu (14.31% ) 183.951 amu (30.64% ) 185.954 amu (28.43% )

To identify the element based on its isotopic masses and abundances, we calculate the **weighted average atomic mass** of the element. The formula for the weighted average atomic mass is:<br /><br />\[<br />\text{Weighted Average Atomic Mass} = \sum (\text{Isotopic Mass} \times \text{Fractional Abundance})<br />\]<br /><br />### Step 1: Convert Percent Abundances to Fractions<br />The given percent abundances are converted into fractional abundances by dividing each percentage by 100:<br /><br />- \( 0.12\% = 0.0012 \)<br />- \( 26.50\% = 0.2650 \)<br />- \( 14.31\% = 0.1431 \)<br />- \( 30.64\% = 0.3064 \)<br />- \( 28.43\% = 0.2843 \)<br /><br />### Step 2: Multiply Each Isotopic Mass by Its Fractional Abundance<br />Now, multiply each isotopic mass by its corresponding fractional abundance:<br /><br />1. \( 179.947 \times 0.0012 = 0.2159364 \)<br />2. \( 181.948 \times 0.2650 = 48.260220 \)<br />3. \( 182.950 \times 0.1431 = 26.191845 \)<br />4. \( 183.951 \times 0.3064 = 56.3874464 \)<br />5. \( 185.954 \times 0.2843 = 52.8726322 \)<br /><br />### Step 3: Add the Results<br />Add all the contributions from each isotope:<br /><br />\[<br />0.2159364 + 48.260220 + 26.191845 + 56.3874464 + 52.8726322 = 183.928080<br />\]<br /><br />### Step 4: Identify the Element<br />The calculated weighted average atomic mass is approximately **183.93 amu**, which corresponds to the element **Tungsten (W)** on the periodic table.<br /><br />### Final Answer:<br />The element is **Tungsten (W)**.