To calculate the relative atomic mass (A_r) of bromine considering its isotopes \(^{79}{35}Br\) and \(^{81}{35}Br\), we use the following formula:
\[ A_r = \left( \frac{\text{abundance of } ^{79}Br}{100} \times \text{mass of } ^{79}Br \right) + \left( \frac{\text{abundance of } ^{81}Br}{100} \times \text{mass of } ^{81}Br \right) \]
Given:
- Mass of \(^{79}Br = 79\)
- Mass of \(^{81}Br = 81\)
- Abundance of \(^{79}Br = 50.7%\)
- Abundance of \(^{81}Br = 49.3%\)
Now, we can substitute these values into the formula:
\[ A_r = \left( \frac{50.7}{100} \times 79 \right) + \left( \frac{49.3}{100} \times 81 \right) \]
Calculating each term:
\[ A_r = (0.507 \times 79) + (0.493 \times 81) \] \[ A_r = 40.113 + 39.873 \] \[ A_r = 79.986 \]
Finally, rounding to three significant figures, we get:
\[ \text{Relative atomic mass (A_r)} \approx 80.0 \]
Thus, the relative atomic mass of bromine is 80.0 (to 3 significant figures).