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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 gives information about these isotopes.

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

The average atomic mass of element [tex]$X$[/tex] is [tex]$\boxed{\hspace{2cm}}$[/tex] amu.



Answer :

GinnyAnswer
To determine the average atomic mass of element [tex]\( X \)[/tex], you need to consider both the atomic masses and their corresponding abundances of its isotopes.

Here is the detailed, step-by-step solution:

1. Convert the percentage abundances to decimals:
[tex]\[ \text{Abundance of } X-63 = \frac{69.15}{100} = 0.6915 \][/tex]
[tex]\[ \text{Abundance of } X-65 = \frac{30.85}{100} = 0.3085 \][/tex]

2. Use the formula for average atomic mass:
[tex]\[ \text{Average Atomic Mass} = (\text{mass of isotope 1} \times \text{abundance of isotope 1}) + (\text{mass of isotope 2} \times \text{abundance of isotope 2}) \][/tex]

3. Insert the given data into the formula:
[tex]\[ \text{Average Atomic Mass} = (62.9296 \times 0.6915) + (64.9278 \times 0.3085) \][/tex]

4. Calculate the contributions of each isotope:
[tex]\[ 62.9296 \times 0.6915 \approx 43.493 \][/tex]
[tex]\[ 64.9278 \times 0.3085 \approx 20.057 \][/tex]

5. Add these contributions to find the total average atomic mass:
[tex]\[ 43.493 + 20.057 \approx 63.55 \][/tex]

6. Round to the nearest hundredth if necessary:

Thus, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( \boxed{63.55} \, \text{amu} \)[/tex].

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