# Problem: Boron has only two naturally occurring isotopes. The mass of boron-10 is 10.01294 amu and the mass of boron-11 is 11.00931 amu .Use the atomic mass of boron to calculate the relative abundance of boron-11.

###### FREE Expert Solution

We’re given the following values:

Average Atomic Mass = 10.821 amu  (found in books or the internet)

Boron-10: Mass = 10.01294 amu

Boron-11: Mass = 11.00931 amu

We don’t know the percent abundance of boron but we can use the fact that the f.a. of all isotopes of an element add up to 1

Since there are only two isotopes, this means:

Boron-10:      f.a. = x

Boron-11:    f.a. = 1 – x

Solving for x:

$\mathbf{10}\mathbf{.}\mathbf{821}\mathbf{=}\mathbf{10}\mathbf{.}\mathbf{01294}\mathbf{x}\mathbf{+}\mathbf{11}\mathbf{.}\mathbf{00931}\mathbf{-}\mathbf{11}\mathbf{.}\mathbf{00931}\mathbf{x}\phantom{\rule{0ex}{0ex}}\mathbf{10}\mathbf{.}\mathbf{821}\mathbf{-}\mathbf{11}\mathbf{.}\mathbf{00931}\mathbf{=}\mathbf{10}\mathbf{.}\mathbf{01294}\mathbf{x}\mathbf{-}\mathbf{11}\mathbf{.}\mathbf{00931}\mathbf{x}\phantom{\rule{0ex}{0ex}}\frac{\overline{)\mathbf{-}}\mathbf{0}\mathbf{.}\mathbf{18831}}{\overline{)\mathbf{-}}\mathbf{0}\mathbf{.}\mathbf{99637}}\mathbf{=}\frac{\overline{)\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{99637}}\mathbf{x}}{\overline{)\mathbf{-}\mathbf{0}\mathbf{.}\mathbf{99637}}}$ ###### Problem Details

Boron has only two naturally occurring isotopes. The mass of boron-10 is 10.01294 amu and the mass of boron-11 is 11.00931 amu .

Use the atomic mass of boron to calculate the relative abundance of boron-11.