# Silver has two naturally occurring isotopes with the following isotopic masses 106.90509 and 108.9047. The average atomic mass of silver is 107.8682 amu. What is the fractional abundance of the lighter of the two isotopes?

Feb 5, 2016

This is two equations in 2 unknowns, therefore it is soluble.

#### Explanation:

We know that:

${x}_{1} 106.9059 + {x}_{2} 108.9047 = 107.8682$ $\left(i\right)$

${x}_{1} + {x}_{2} = 1$ $\left(i i\right)$

We assume that silver has only the 2 isotopes, which for a first approximation is true.

From $\left(i i\right)$, $1 - {x}_{2} = {x}_{1}$. So we substitute back into $\left(i\right)$:

$\left(1 - {x}_{2}\right) 106.9059 + {x}_{2} 108.9047 = 107.8682$

So solve for ${x}_{2}$ and find your percentages.