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What is the average atomic mass of the element?

An element, [tex]$X$[/tex], has two isotopes, [tex]$X-14$[/tex] and [tex]$X-15$[/tex]. Use the data in the table to find the average atomic mass of element [tex]$X$[/tex].

\begin{tabular}{|c|c|c|}
\hline Isotope & \begin{tabular}{c}
Atomic \\
Mass
\end{tabular} & \begin{tabular}{c}
Abundance \\
(\%)
\end{tabular} \\
\hline X-14 & 14.003 & 99.636 \\
\hline X-15 & 15.000 & 0.364 \\
\hline
\end{tabular}

The average atomic mass of element [tex]$X$[/tex] is [tex]$\boxed{\phantom{00}}$[/tex] amu.



Answer :

GinnyAnswer
To find the average atomic mass of an element with isotopes, you follow these steps:

1. Identify the atomic masses and their respective abundances.
- For isotope [tex]\( X-14 \)[/tex]:
- Atomic mass: 14.003 amu
- Abundance: 99.636%
- For isotope [tex]\( X-15 \)[/tex]:
- Atomic mass: 15.000 amu
- Abundance: 0.364%

2. Convert the abundances from percentages to fractions:
[tex]\[ \text{Abundance of } X-14 = \frac{99.636}{100} = 0.99636 \][/tex]
[tex]\[ \text{Abundance of } X-15 = \frac{0.364}{100} = 0.00364 \][/tex]

3. Multiply each atomic mass by its respective fractional abundance to find the contribution of each isotope to the average atomic mass:
[tex]\[ \text{Contribution of } X-14 = 14.003 \times 0.99636 = 13.95194668 \, \text{amu} \][/tex]
[tex]\[ \text{Contribution of } X-15 = 15.000 \times 0.00364 = 0.0546824 \, \text{amu} \][/tex]

4. Add the contributions of the isotopes to find the average atomic mass:
[tex]\[ \text{Average atomic mass} = 13.95194668 + 0.0546824 = 14.00662908 \, \text{amu} \][/tex]

5. Round the result to the nearest thousandth:
[tex]\[ \text{Average atomic mass} \approx 14.007 \, \text{amu} \][/tex]

Hence, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( 14.007 \, \text{amu} \)[/tex].

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