Question

Rubidium has two naturally occurring isotopes, rubidium- 85 (atomic mass \(=84.9118\) amu; abundance \(=72.15 \%\) ) and rubidium-87 (atomic mass \(=86.9092\) amu; abundance \(=27.85 \%\) ). Calculate the atomic weight of rubidium.

Short answer

The atomic weight of rubidium is approximately \(85.494\) amu.

Step-by-step solution

Find the weighted atomic mass for each isotope

To find the weighted atomic mass for each isotope, we need to multiply the atomic mass by its relative abundance. Convert the percentage of relative abundance into a decimal number by dividing it by 100. Weighted atomic mass of rubidium-85: \(84.9118 \times 0.7215\) Weighted atomic mass of rubidium-87: \(86.9092 \times 0.2785\)

Calculate the atomic weight of rubidium

Add the weighted atomic masses of both isotopes to find the atomic weight of rubidium. Atomic weight = (weighted atomic mass of rubidium-85) + (weighted atomic mass of rubidium-87) Atomic weight = \((84.9118 \times 0.7215) + (86.9092 \times 0.2785)\)

Evaluate the expression

Perform the calculations to find the atomic weight of rubidium. Atomic weight = \((61.2782083) + (24.215607\)) Atomic weight = \(85.4938153\)

Round the result

Round the result to a reasonable number of significant figures. In this case, we can round to 5 significant figures. The atomic weight of rubidium is approximately \(85.494\) amu.