# Calculating percent abundance for 3 isotopes

1. Sep 29, 2011

### Same-same

For my chemistry class, I need to be able to calculate percent abundances for multiples isotopes, if given the mass of the isotopes and average atomic mass of the element. The percent abundance of 1 isotope may be given.

The teacher has said that calculating for a problem with 3 isotopes is all that will be required. However, if possible, I would like to be able to solve a problem with more isotopes, just for future courses.
I tried setting up the equation, and I searched my textbook, and have gotten nowhere. The teacher reccomended I search the internet, and I still have gotten nowhere.

Can anyone show me how one solves such a problem?
Thanks.

2. Sep 30, 2011

### Staff: Mentor

If I understand your question correctly, it can't be done the way you want it.

To solve system of simultaneous equations you need to have as many equations as unknowns (it still doesn't guarantee there will be a solution, but if there is not enough equations, you can be sure there is no unique solution). If there are less equations we call it an http://en.wikipedia.org/wiki/Underdetermined_system.

You have always two equations - one is that sum of abundances is 100%, the other one is average atomic mass.

If there are two isotopes, you have two equations and two unknowns - and solving the problem is not difficult.

If there are three isotopes you have three unknowns and two equations - and that means you can't solve it. If you are given abundance of a third isotope, that is equivalent of having a third equation.

Last edited: Sep 30, 2011
3. Sep 30, 2011

### Same-same

Okay, that must be what we need to able to figure out
Thanks!