To find the average atomic mass of element [tex]$X$[/tex], we follow these steps:
1. Convert the abundance percentages to proportions:
- For isotope X-63, the abundance is 69.15%, which as a proportion is [tex]\( \frac{69.15}{100} = 0.6915 \)[/tex].
- For isotope X-65, the abundance is 30.85%, which as a proportion is [tex]\( \frac{30.85}{100} = 0.3085 \)[/tex].
2. Calculate the weighted average atomic mass:
[tex]\[
\text{Average atomic mass} = (\text{Atomic mass of X-63} \times \text{Proportion of X-63}) + (\text{Atomic mass of X-65} \times \text{Proportion of X-65})
\][/tex]
Substituting the values:
[tex]\[
\text{Average atomic mass} = (62.9296 \times 0.6915) + (64.9278 \times 0.3085)
\][/tex]
[tex]\[
\text{Average atomic mass} = 43.5196124 + 20.0264323
\][/tex]
[tex]\[
\text{Average atomic mass} = 63.5460447
\][/tex]
3. Round the result to the nearest hundredth:
The unrounded average atomic mass is 63.5460447. When we round this to the nearest hundredth, we get 63.55.
Therefore, the average atomic mass of element [tex]\(X\)[/tex] is [tex]\( \boxed{63.55} \)[/tex] amu.
