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

Element [tex]\( X \)[/tex] has two isotopes. The table provides information about these isotopes.

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

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



Answer :

GinnyAnswer
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.

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