To calculate the average atomic mass of rubidium based on the isotopes and their abundances, we can use the following formula:
\[ \text{Average atomic mass} = \left( \text{isotope mass} \times \text{abundance} \right) + \left( \text{isotope mass} \times \text{abundance} \right) \]
Given the isotopes:
- \(^85 Rb\) with an abundance of 80.2%
- \(^87 Rb\) with an abundance of 19.8%
We'll use the approximate masses of the isotopes:
- Mass of \(^85 Rb\) = 84.911 amu
- Mass of \(^87 Rb\) = 86.909 amu
First, we convert the percentage abundances to decimal form:
- Abundance of \(^85 Rb\) = 80.2% = 0.802
- Abundance of \(^87 Rb\) = 19.8% = 0.198
Now we can calculate the average atomic mass:
\[ \text{Average atomic mass} = (84.911 , \text{amu} \times 0.802) + (86.909 , \text{amu} \times 0.198) \]
Calculating each term:
- \(84.911 , \text{amu} \times 0.802 = 68.169822 , \text{amu}\)
- \(86.909 , \text{amu} \times 0.198 = 17.233782 , \text{amu}\)
Now, add these two results together:
\[ \text{Average atomic mass} = 68.169822 , \text{amu} + 17.233782 , \text{amu} = 85.403604 , \text{amu} \]
Thus, the average atomic mass of rubidium is approximately \(85.40 , \text{amu}\).