# The fictional isotope Xium-60 has an atomic mass of 60.15 units while Xium-70 has an atomic mass of 70.16 units. The average mass of Xium is 69.41 units. What is the fractional abundance of Xium 70? Assume that only these two isotopes of Xium occur in nature.

The average atomic mass of an element, which in this case is 69.41 units, is weighted to reflect the relative abundance of each isotope in nature. It's the sum of the mass of each isotope multiplied by its percent or fractional abundance:

(60.15 x fractional abundance) + (70.16 x fractional abundance) = 69.41

We can express the unknown fractional abundance of each isotope in terms of the same variable because we know that their sum is 1 or 100%:

fractional abundance of Xium 70 = x

fractional abundance of Xium 60 = 1-x

Now we can substitute x and 1-x into the equation and solve for x:

(60.15)(1-x) + (70.16)(x) = 69.41

60.15 - 60.15x + 70.16x = 69.41

10.01x = 9.26

x = 0.9251

fractional abundance of Xium-70 = 0.9251 or 92.51%

fractional abundance of Xium-60 = 0.0749 or 7.49%