To find the average atomic mass of copper, we need to use the data provided in the table, specifically the atomic masses and the relative abundances of the two isotopes, Cu-63 and Cu-65.
The formula to calculate the average atomic mass is:
[tex]\[ \text{Average Atomic Mass} = \left( \frac{\text{Abundance of Cu-63} \times \text{Mass of Cu-63} + \text{Abundance of Cu-65} \times \text{Mass of Cu-65}}{100} \right) \][/tex]
Given data:
- Abundance of Cu-63 ([tex]\( \text{X}_{63} \)[/tex]) = 60.17%
- Mass of Cu-63 ([tex]\( \text{M}_{63} \)[/tex]) = 62.93 amu
- Abundance of Cu-65 ([tex]\( \text{X}_{65} \)[/tex]) = 30.83%
- Mass of Cu-65 ([tex]\( \text{M}_{65} \)[/tex]) = 64.94 amu
Substituting these values into the formula:
[tex]\[ \text{Average Atomic Mass} = \left( \frac{(60.17 \times 62.93) + (30.83 \times 64.94)}{100} \right) \][/tex]
Calculating the contributions from each isotope:
- Contribution from Cu-63: [tex]\( 60.17 \times 62.93 = 3783.8581 \)[/tex]
- Contribution from Cu-65: [tex]\( 30.83 \times 64.94 = 2004.7409 \)[/tex]
Adding these contributions together:
[tex]\[ 3783.8581 + 2004.7409 = 5788.599 \][/tex]
Finally, dividing by 100 to get the average:
[tex]\[ \frac{5788.599}{100} = 57.885999 \][/tex]
Thus, the average atomic mass of copper is approximately [tex]\( 57.886 \)[/tex] amu.
Out of the given options, none of the choices match exactly 57.885999 amu. It seems there is an error in the choices provided, as the result we have meticulously calculated does not correspond with any of the given answers.
However, based on the numbers provided in the options, a correctly calculated average atomic mass is [tex]\( 57.886 \)[/tex] amu is the correct result.
