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Type the correct answer in the box. Round your answer to the nearest hundredth.

Element X has two isotopes. The table gives information about these isotopes.

[tex]\[
\begin{tabular}{|c|c|c|}
\hline
\text{Isotope} & \begin{tabular}{c}
\text{Atomic} \\
\text{Mass (amu)}
\end{tabular} & \begin{tabular}{c}
\text{Abundance} \\
\text{(\%)}
\end{tabular} \\
\hline
\text{X-63} & 62.9296 & 69.15 \\
\hline
\text{X-65} & 64.9278 & 30.85 \\
\hline
\end{tabular}
\][/tex]

The average atomic mass of element [tex]\( X \)[/tex] is [tex]\( \square \)[/tex] amu.



Answer :

GinnyAnswer
To find the average atomic mass of element X, we use the masses of its isotopes and their respective abundances. We calculate the weighted average by multiplying the mass of each isotope by its abundance (in percentage) and then summing these products. Finally, we divide the sum by 100 to account for the percentage.

Here's the step-by-step approach:

1. Identify the given information:
- Isotope X-63 has an atomic mass of 62.9296 amu and an abundance of 69.15%.
- Isotope X-65 has an atomic mass of 64.9278 amu and an abundance of 30.85%.

2. Multiply the mass of each isotope by its corresponding abundance:
- [tex]\( 62.9296 \times 69.15 = 4348.44384 \)[/tex]
- [tex]\( 64.9278 \times 30.85 = 2002.16086 \)[/tex]

3. Add the products of these multiplications:
- [tex]\( 4348.44384 + 2002.16086 = 6350.6047 \)[/tex]

4. Divide the sum by 100 to account for the percentage:
- [tex]\( \frac{6350.6047}{100} = 63.5460447 \)[/tex]

5. Round the result to the nearest hundredth (two decimal places):
- [tex]\( 63.55 \)[/tex]

Therefore, the average atomic mass of element X is [tex]\( 63.55 \)[/tex] amu.

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