Questions: A certain element consists of two stable isotopes. The first has a mass of 78.9 amu and a percent natural abundance of 50.5%. The second has a mass of 80.9 amu and a percent natural abundance of 49.5%. What is the atomic weight of the element? amu

A certain element consists of two stable isotopes. The first has a mass of 78.9 amu and a percent natural abundance of 50.5%. The second has a mass of 80.9 amu and a percent natural abundance of 49.5%. What is the atomic weight of the element? amu
Transcript text: A certain element consists of two stable isotopes. The first has a mass of $\mathbf{7 8 . 9} \mathrm{amu}$ and a percent natural abundance of $\mathbf{5 0 . 5} \%$. The second has a mass of $\mathbf{8 0 . 9} \mathrm{amu}$ and a percent natural abundance of $\mathbf{4 9 . 5} \%$. What is the atomic weight of the element? $\square$ amu
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Solution

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Solution Steps

Step 1: Understand the Concept of Atomic Weight

The atomic weight of an element is the weighted average of the masses of its isotopes, based on their natural abundances. This can be calculated using the formula:

\[ \text{Atomic Weight} = \sum (\text{isotope mass} \times \text{fractional abundance}) \]

Step 2: Convert Percent Abundances to Fractions

Convert the percent natural abundances of the isotopes to fractional abundances by dividing by 100.

  • For the first isotope: \(50.5\% = 0.505\)
  • For the second isotope: \(49.5\% = 0.495\)
Step 3: Calculate the Contribution of Each Isotope

Calculate the contribution of each isotope to the atomic weight by multiplying the mass of each isotope by its fractional abundance.

  • Contribution of the first isotope: \[ 78.9 \, \text{amu} \times 0.505 = 39.8445 \, \text{amu} \]

  • Contribution of the second isotope: \[ 80.9 \, \text{amu} \times 0.495 = 40.0455 \, \text{amu} \]

Step 4: Sum the Contributions to Find the Atomic Weight

Add the contributions of each isotope to find the atomic weight of the element.

\[ \text{Atomic Weight} = 39.8445 \, \text{amu} + 40.0455 \, \text{amu} = 79.8900 \, \text{amu} \]

Final Answer

The atomic weight of the element is \(\boxed{79.8900 \, \text{amu}}\).

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