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].
