To find the average atomic mass of element [tex]$X$[/tex] given the two isotopes, we need to perform a weighted average calculation. Here are the steps:
1. Identify the masses and their corresponding abundances:
- Isotope X-63 has a mass of 62.9296 amu and an abundance of 69.15%.
- Isotope X-65 has a mass of 64.9278 amu and an abundance of 30.85%.
2. Convert abundance percentages to fractions:
- Abundance of X-63 as a fraction: [tex]\( \frac{69.15}{100} = 0.6915 \)[/tex]
- Abundance of X-65 as a fraction: [tex]\( \frac{30.85}{100} = 0.3085 \)[/tex]
3. Calculate the weighted average:
We multiply each mass by its corresponding fraction and then add the results:
[tex]\[
\text{Average Atomic Mass} = (62.9296 \times 0.6915) + (64.9278 \times 0.3085)
\][/tex]
4. Perform the multiplication and addition:
- For X-63: [tex]\( 62.9296 \times 0.6915 = 43.5112 \)[/tex]
- For X-65: [tex]\( 64.9278 \times 0.3085 = 20.0348 \)[/tex]
- Add these values: [tex]\( 43.5112 + 20.0348 = 63.546 \)[/tex]
5. Round the result to the nearest hundredth:
- The average atomic mass rounded to the nearest hundredth is [tex]\( 63.55 \)[/tex].
Therefore, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( 63.55 \)[/tex] amu.
