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Calculate the average atomic mass of element [tex]\(X\)[/tex].

The table below provides information about the isotopes of element [tex]\(X\)[/tex].

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

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

Sagot :

GinnyAnswer
To find the average atomic mass of element [tex]$X$[/tex] given the two isotopes, we need to perform a weighted average calculation. Here are the steps:

1. Identify the masses and their corresponding abundances:
- Isotope X-63 has a mass of 62.9296 amu and an abundance of 69.15%.
- Isotope X-65 has a mass of 64.9278 amu and an abundance of 30.85%.

2. Convert abundance percentages to fractions:
- Abundance of X-63 as a fraction: [tex]\( \frac{69.15}{100} = 0.6915 \)[/tex]
- Abundance of X-65 as a fraction: [tex]\( \frac{30.85}{100} = 0.3085 \)[/tex]

3. Calculate the weighted average:
We multiply each mass by its corresponding fraction and then add the results:
[tex]\[ \text{Average Atomic Mass} = (62.9296 \times 0.6915) + (64.9278 \times 0.3085) \][/tex]

4. Perform the multiplication and addition:
- For X-63: [tex]\( 62.9296 \times 0.6915 = 43.5112 \)[/tex]
- For X-65: [tex]\( 64.9278 \times 0.3085 = 20.0348 \)[/tex]
- Add these values: [tex]\( 43.5112 + 20.0348 = 63.546 \)[/tex]

5. Round the result to the nearest hundredth:
- The average atomic mass rounded to the nearest hundredth is [tex]\( 63.55 \)[/tex].

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