To determine the average atomic mass of element [tex]\( X \)[/tex], we need to consider the atomic masses and the relative abundances of its isotopes. Given the data in the table, we have:
- Isotope [tex]\( X-14 \)[/tex] with atomic mass [tex]\( 14.003 \)[/tex] amu and abundance [tex]\( 99.636\% \)[/tex].
- Isotope [tex]\( X-15 \)[/tex] with atomic mass [tex]\( 15.000 \)[/tex] amu and abundance [tex]\( 0.364\% \)[/tex].
We'll follow these steps:
1. Convert the percentage abundances to decimal fractions:
- Abundance of [tex]\( X-14 \)[/tex]: [tex]\( \frac{99.636}{100} = 0.99636 \)[/tex]
- Abundance of [tex]\( X-15 \)[/tex]: [tex]\( \frac{0.364}{100} = 0.00364 \)[/tex]
2. Calculate the average atomic mass by multiplying each isotope's atomic mass by its corresponding fractional abundance and then adding the results:
- Contribution of [tex]\( X-14 \)[/tex] to the average atomic mass: [tex]\( 14.003 \times 0.99636 = 13.95386908\)[/tex]
- Contribution of [tex]\( X-15 \)[/tex] to the average atomic mass: [tex]\( 15.000 \times 0.00364 = 0.05454\)[/tex]
3. Summing these contributions gives:
- [tex]\( 13.95386908 + 0.05454 = 14.00840908 \)[/tex]
4. Finally, we round this result to the nearest thousandth:
- [tex]\( 14.00840908 \)[/tex] rounded to the nearest thousandth is [tex]\( 14.008 \)[/tex]
Therefore, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( 14.008 \)[/tex] amu.
The average atomic mass of element [tex]\( X \)[/tex] is [tex]\( \boxed{14.007} \)[/tex] amu.
