To find the average atomic mass of element [tex]\( X \)[/tex], we need to use the masses of the isotopes and their respective abundances. The average atomic mass is calculated using the formula for the weighted average:
[tex]\[
\text{average atomic mass} = \left( \frac{\text{mass of isotope 1} \times \text{abundance of isotope 1}}{100} \right) + \left( \frac{\text{mass of isotope 2} \times \text{abundance of isotope 2}}{100} \right)
\][/tex]
Firstly, let's identify the masses and abundances given:
- 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%.
Now, convert the percentage abundances to decimal form by dividing by 100:
- The abundance of X-63 is [tex]\( \frac{69.15}{100} = 0.6915 \)[/tex].
- The abundance of X-65 is [tex]\( \frac{30.85}{100} = 0.3085 \)[/tex].
Next, we calculate the contribution of each isotope to the average atomic mass:
- Contribution of X-63: [tex]\( 62.9296 \times 0.6915 = 43.5048 \)[/tex]
- Contribution of X-65: [tex]\( 64.9278 \times 0.3085 = 20.04695 \)[/tex]
Adding these contributions together gives the average atomic mass:
[tex]\[
43.5048 + 20.04695 = 63.55175
\][/tex]
Finally, we round this result to the nearest hundredth:
[tex]\[
63.55175 \approx 63.55
\][/tex]
Therefore, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( 63.55 \)[/tex] amu.
