To determine the average atomic mass of element X, we need to use the atomic masses and their respective abundances provided in the table.
Here’s the step-by-step process:
1. Identify the atomic mass and abundance of each isotope:
- Isotope X-63 has an atomic mass of 62.9296 amu and an abundance of 69.15%.
- Isotope X-65 has an atomic mass of 64.9278 amu and an abundance of 30.85%.
2. Convert the abundance 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 from X-63: [tex]\( 62.9296 \times 0.6915 \)[/tex]
- Contribution from X-65: [tex]\( 64.9278 \times 0.3085 \)[/tex]
4. Add the contributions to get the average atomic mass:
[tex]\[
\text{Average atomic mass} = (62.9296 \times 0.6915) + (64.9278 \times 0.3085)
\][/tex]
5. Perform the multiplications and addition to find the average atomic mass:
- [tex]\( 62.9296 \times 0.6915 = 43.5051 \)[/tex]
- [tex]\( 64.9278 \times 0.3085 = 20.0449 \)[/tex]
Adding these values together gives:
[tex]\[
43.5051 + 20.0449 = 63.55
\][/tex]
6. Round the average atomic mass to the nearest hundredth:
- The average atomic mass of element X, rounded to the nearest hundredth, is 63.55 amu.
Hence, the average atomic mass of element X is [tex]\( \boxed{63.55} \)[/tex] amu.
