To calculate the average atomic mass of element [tex]\( X \)[/tex], we need to use the given data for its isotopes. We will calculate the weighted mass contribution from each isotope and then sum these contributions.
1. Isotope [tex]\( X-63 \)[/tex]:
- Atomic mass: 62.9296 amu
- Abundance: 69.15%
2. Isotope [tex]\( X-65 \)[/tex]:
- Atomic mass: 64.9278 amu
- Abundance: 30.85%
Step 1: Calculate the weighted mass contribution of each isotope.
For isotope [tex]\( X-63 \)[/tex]:
[tex]\[
\text{Weighted mass of } X-63 = \text{Atomic mass of } X-63 \times \left(\frac{\text{Abundance of } X-63}{100}\right)
\][/tex]
[tex]\[
\text{Weighted mass of } X-63 = 62.9296 \times \left(\frac{69.15}{100}\right) = 43.5158184 \, \text{amu}
\][/tex]
For isotope [tex]\( X-65 \)[/tex]:
[tex]\[
\text{Weighted mass of } X-65 = \text{Atomic mass of } X-65 \times \left(\frac{\text{Abundance of } X-65}{100}\right)
\][/tex]
[tex]\[
\text{Weighted mass of } X-65 = 64.9278 \times \left(\frac{30.85}{100}\right) = 20.0302263 \, \text{amu}
\][/tex]
Step 2: Add the weighted mass contributions to determine the average atomic mass.
[tex]\[
\text{Average atomic mass} = \text{Weighted mass of } X-63 + \text{Weighted mass of } X-65
\][/tex]
[tex]\[
\text{Average atomic mass} = 43.5158184 \, \text{amu} + 20.0302263 \, \text{amu} = 63.5460447 \, \text{amu}
\][/tex]
Step 3: Round the average atomic mass to the nearest hundredth.
[tex]\[
63.5460447 \, \text{amu} \approx 63.55 \, \text{amu}
\][/tex]
Therefore, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( \boxed{63.55} \, \text{amu} \)[/tex].
