What is the average atomic mass of the element in the data table?

\begin{tabular}{|c|c|}
\hline Mass (amu) & Abundance (\%) \\
\hline 20.0 & 90.480 \\
\hline 21.0 & 0.270 \\
\hline 22.0 & 9.250 \\
\hline
\end{tabular}

A. 67.2 amu
B. 20.2 amu
C. 16.0 amu
D. 35.5 amu



Answer :

To determine the average atomic mass of the element given its isotopes and their respective abundances, we follow these steps:

1. List the mass and abundance of each isotope.

Here, we have:
- Isotope with mass 20.0 amu and abundance 90.480%
- Isotope with mass 21.0 amu and abundance 0.270%
- Isotope with mass 22.0 amu and abundance 9.250%

2. Convert the percentages into fractions (i.e., divide each percentage by 100).

- 90.480% becomes 0.90480
- 0.270% becomes 0.00270
- 9.250% becomes 0.09250

3. Multiply the mass of each isotope by its fractional abundance to find the weighted contribution of each isotope to the average atomic mass.

- For the isotope with mass 20.0 amu:
[tex]\[ 20.0 \times 0.90480 = 18.096 \][/tex]

- For the isotope with mass 21.0 amu:
[tex]\[ 21.0 \times 0.00270 = 0.0567 \][/tex]

- For the isotope with mass 22.0 amu:
[tex]\[ 22.0 \times 0.09250 = 2.035 \][/tex]

4. Sum these contributions to get the average atomic mass.

[tex]\[ \text{Average atomic mass} = 18.096 + 0.0567 + 2.035 = 20.1877 \][/tex]

So, the average atomic mass of the element is [tex]\(20.1877 \text{ amu}\)[/tex].