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Difficulty: MediumRelative Atomic Mass, Relative Molecular Mass, and Carbon-12 Scale

A naturally occurring sample of boron consists of two stable isotopes, 10B^{10}\text{B} and 11B^{11}\text{B}. If the relative percentage abundance of 10B^{10}\text{B} is 20.0%20.0\% and that of 11B^{11}\text{B} is 80.0%80.0\%, what is the relative atomic mass of boron?

Answer: 10.8

Answer

The relative atomic mass of boron is 10.810.8.
The relative atomic mass of an element is defined as the weighted average mass of its naturally occurring isotopes relative to 112th\frac{1}{12}\text{th} the mass of a carbon-12 atom. Applying the formula RAM=∑(isotopic mass×% abundance)100\text{RAM} = \frac{\sum (\text{isotopic mass} \times \% \text{ abundance})}{100}, we get (10×20)+(11×80)100=200+880100=10.8\frac{(10 \times 20) + (11 \times 80)}{100} = \frac{200 + 880}{100} = 10.8.

Step-by-Step Solution

1
Determine the mass contribution of the 10B^{10}\text{B} isotope
10×0.20=2.010 \times 0.20 = 2.0
The weighted contribution of an isotope is its mass multiplied by its fractional abundance.
2
Determine the mass contribution of the 11B^{11}\text{B} isotope
11×0.80=8.811 \times 0.80 = 8.8
The weighted contribution of the second isotope is calculated using its percentage abundance.
3
Sum the weighted contributions to find the relative atomic mass
2.0+8.8=10.82.0 + 8.8 = 10.8
The relative atomic mass of an element is the weighted average mass of all naturally occurring isotopes relative to carbon-12.

Key Concept

Calculation of Relative Atomic Mass from Isotopic Abundances
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Topics

Relative Atomic Mass, Relative Molecular Mass, and Carbon-12 Scale

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