To calculate the relative atomic mass (A_r) for copper based on its isotopes, you can use the following formula:
\[ A_r = \left( \frac{\text{(mass of isotope 1)} \times \text{(abundance of isotope 1)}}{100} \right) + \left( \frac{\text{(mass of isotope 2)} \times \text{(abundance of isotope 2)}}{100} \right) \]
For copper:
- Isotope \(^{63}_{29}\text{Cu}\) (mass = 63 amu) with abundance = 69.2%
- Isotope \(^{65}_{29}\text{Cu}\) (mass = 65 amu) with abundance = 30.8%
Now substitute the values into the formula:
\[ A_r = \left( 63 \times 69.2 \right) + \left( 65 \times 30.8 \right) \]
Calculating each part:
-
For \(^{63}_{29}\text{Cu}\): \[ 63 \times 69.2 = 4365.6 \]
-
For \(^{65}_{29}\text{Cu}\): \[ 65 \times 30.8 = 2002.0 \]
Now add these two results:
\[ A_r = 4365.6 + 2002.0 = 6367.6 \]
Now we calculate the overall atomic mass by dividing by 100 (to account for the percentage):
\[ A_r = \frac{6367.6}{100} = 63.676 \]
Rounding to three significant figures:
\[ A_r \approx 63.7 \]
Thus, the relative atomic mass (A_r) of copper to three significant figures is 63.7.
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