To find the average atomic mass of an element with isotopes, you follow these steps:
1. Identify the atomic masses and their respective abundances.
- For isotope [tex]\( X-14 \)[/tex]:
- Atomic mass: 14.003 amu
- Abundance: 99.636%
- For isotope [tex]\( X-15 \)[/tex]:
- Atomic mass: 15.000 amu
- Abundance: 0.364%
2. Convert the abundances from percentages to fractions:
[tex]\[
\text{Abundance of } X-14 = \frac{99.636}{100} = 0.99636
\][/tex]
[tex]\[
\text{Abundance of } X-15 = \frac{0.364}{100} = 0.00364
\][/tex]
3. Multiply each atomic mass by its respective fractional abundance to find the contribution of each isotope to the average atomic mass:
[tex]\[
\text{Contribution of } X-14 = 14.003 \times 0.99636 = 13.95194668 \, \text{amu}
\][/tex]
[tex]\[
\text{Contribution of } X-15 = 15.000 \times 0.00364 = 0.0546824 \, \text{amu}
\][/tex]
4. Add the contributions of the isotopes to find the average atomic mass:
[tex]\[
\text{Average atomic mass} = 13.95194668 + 0.0546824 = 14.00662908 \, \text{amu}
\][/tex]
5. Round the result to the nearest thousandth:
[tex]\[
\text{Average atomic mass} \approx 14.007 \, \text{amu}
\][/tex]
Hence, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( 14.007 \, \text{amu} \)[/tex].
