To find the average atomic mass of element X given the data for its two isotopes, we follow these steps:
1. Identify the mass and abundance of each isotope:
- The atomic mass of isotope X-63 is 62.9296 amu.
- The abundance of isotope X-63 is 69.15%.
- The atomic mass of isotope X-65 is 64.9278 amu.
- The abundance of isotope X-65 is 30.85%.
2. Convert the abundance percentages into decimal fractions:
- The abundance of isotope X-63 as a fraction is [tex]\( 69.15\% \)[/tex] or [tex]\( 0.6915 \)[/tex].
- The abundance of isotope X-65 as a fraction is [tex]\( 30.85\% \)[/tex] or [tex]\( 0.3085 \)[/tex].
3. Calculate the weighted average of the atomic masses:
- Multiply the atomic mass of each isotope by its respective fraction.
- For isotope X-63: [tex]\( 62.9296 \times 0.6915 \)[/tex].
- For isotope X-65: [tex]\( 64.9278 \times 0.3085 \)[/tex].
4. Sum the weighted masses to find the average atomic mass:
- Average atomic mass = [tex]\( (62.9296 \times 0.6915) + (64.9278 \times 0.3085) \)[/tex].
5. Round the result to the nearest hundredth:
- After performing the calculations and summing the results, we obtain an average atomic mass of 63.55 amu.
Therefore, the average atomic mass of element X is [tex]\( \boxed{63.55} \)[/tex] amu.
