Sure, I will provide you with a step-by-step solution.
Step 1: Understand the given values.
We are provided with two isotopes of rubidium:
- Rubidium-85 with an atomic mass of 84.9118 amu and an abundance of 72.15%.
- Rubidium-87 with an atomic mass of 86.9092 amu and an abundance of 27.85%.
Step 2: Convert the percentage abundances to decimal form.
- The abundance of rubidium-85:
[tex]\( 72.15\% = 0.7215 \)[/tex] (as a decimal)
- The abundance of rubidium-87:
[tex]\( 27.85\% = 0.2785 \)[/tex] (as a decimal)
Step 3: Apply the formula to calculate the atomic weight.
The atomic weight [tex]\( A \)[/tex] of an element that has multiple isotopes can be calculated using the formula:
[tex]\[ A = (\text{atomic mass of isotope 1} \times \text{abundance of isotope 1}) + (\text{atomic mass of isotope 2} \times \text{abundance of isotope 2}) \][/tex]
Plugging in the values:
[tex]\[ A = (84.9118 \times 0.7215) + (86.9092 \times 0.2785) \][/tex]
Step 4: Calculate the contributions of each isotope.
- Contribution of rubidium-85:
[tex]\[ 84.9118 \times 0.7215 = 61.2972947 \][/tex]
- Contribution of rubidium-87:
[tex]\[ 86.9092 \times 0.2785 = 24.1707812 \][/tex]
Step 5: Sum the contributions to find the atomic weight.
[tex]\[ \text{Atomic weight of rubidium} = 61.2972947 + 24.1707812 = 85.4680759 \][/tex]
So, the atomic weight of rubidium is [tex]\( 85.4680759 \)[/tex] amu.
