To determine the average atomic mass of element [tex]\( X \)[/tex], we need to use the information provided about its isotopes' atomic masses and their respective abundances. We will follow the steps below:
1. Identify the atomic masses and their respective abundances from the table:
- Isotope [tex]\( X \)[/tex]-63 has an atomic mass of 62.9296 amu and an abundance of 69.15%.
- Isotope [tex]\( X \)[/tex]-65 has an atomic mass of 64.9278 amu and an abundance of 30.85%.
2. Convert the percentages of abundance into decimal form by dividing by 100:
- [tex]\( 69.15\% = \frac{69.15}{100} = 0.6915 \)[/tex]
- [tex]\( 30.85\% = \frac{30.85}{100} = 0.3085 \)[/tex]
3. Calculate the contribution of each isotope to the average atomic mass:
- Contribution of [tex]\( X \)[/tex]-63: [tex]\( 62.9296 \times 0.6915 \)[/tex]
- Contribution of [tex]\( X \)[/tex]-65: [tex]\( 64.9278 \times 0.3085 \)[/tex]
4. Add these contributions together to get the total average atomic mass:
[tex]\[
\text{Average atomic mass} = (62.9296 \times 0.6915) + (64.9278 \times 0.3085)
\][/tex]
5. Perform the calculations for the contributions:
[tex]\[
62.9296 \times 0.6915 \approx 43.5102
\][/tex]
[tex]\[
64.9278 \times 0.3085 \approx 20.0398
\][/tex]
6. Sum these contributions to find the total average atomic mass:
[tex]\[
43.5102 + 20.0398 = 63.55
\][/tex]
7. Finally, round the result to the nearest hundredth:
[tex]\[
63.55 \, \text{amu}
\][/tex]
Thus, the average atomic mass of element [tex]\( X \)[/tex] is 63.55 amu.
