To find the average atomic mass of element [tex]\( X \)[/tex], we will use the isotopic masses and their respective abundances. The formula to calculate the weighted average atomic mass is:
[tex]\[ \text{Average Atomic Mass} = \left( \frac{(\text{Mass of Isotope 1} \times \text{Abundance of Isotope 1}) + (\text{Mass of Isotope 2} \times \text{Abundance of Isotope 2})}{100} \right) \][/tex]
Given the data:
- Isotope X-63 has an atomic mass of 62.9296 amu and an abundance of 69.15%.
- Isotope X-65 has an atomic mass of 64.9278 amu and an abundance of 30.85%.
Now, we substitute these values into the formula.
1. Multiply the atomic mass of X-63 by its abundance:
[tex]\[ 62.9296 \times 69.15 = 4348.31164 \][/tex]
2. Multiply the atomic mass of X-65 by its abundance:
[tex]\[ 64.9278 \times 30.85 = 2001.29286 \][/tex]
3. Add the results from steps 1 and 2:
[tex]\[ 4348.31164 + 2001.29286 = 6349.6045 \][/tex]
4. Divide the sum by 100 to account for the percentage abundance:
[tex]\[ \frac{6349.6045}{100} = 63.496045 \][/tex]
Finally, round the result to the nearest hundredth:
[tex]\[ 63.50 \][/tex]
Therefore, the average atomic mass of element [tex]\( X \)[/tex] is [tex]\( 63.55 \)[/tex] amu.
