To determine the average atomic mass of element X, we need to calculate the weighted average mass of its isotopes using their atomic masses and abundances.
Here are the steps to do so:
1. Identify the atomic masses and abundances of the isotopes:
- Isotope X-63: Atomic mass = 62.9296 amu, Abundance = 69.15%
- Isotope X-65: Atomic mass = 64.9278 amu, Abundance = 30.85%
2. Convert the abundances from percentages to decimal form:
- Abundance of X-63 = 69.15% = 0.6915
- Abundance of X-65 = 30.85% = 0.3085
3. Calculate the contribution of each isotope to the average atomic mass:
- Contribution of X-63: [tex]\( 62.9296 \times 0.6915 \)[/tex]
- Contribution of X-65: [tex]\( 64.9278 \times 0.3085 \)[/tex]
4. Sum these contributions to find the weighted average atomic mass:
- Weighted average mass = [tex]\( (62.9296 \times 0.6915) + (64.9278 \times 0.3085) \)[/tex]
5. Perform the calculations:
- Contribution of X-63: [tex]\( 62.9296 \times 0.6915 \approx 43.52 \)[/tex]
- Contribution of X-65: [tex]\( 64.9278 \times 0.3085 \approx 20.03 \)[/tex]
- Sum: [tex]\( 43.52 + 20.03 = 63.55 \)[/tex]
6. Round the result to the nearest hundredth:
- The average atomic mass of element X = 63.55 amu
Thus, the average atomic mass of element X is [tex]\( \boxed{63.55} \)[/tex] amu.
